343 results found
Sun M, Djapic P, Aunedi M, et al., 2019, Benefits of smart control of hybrid heat pumps: an analysis of field trial data, Applied Energy, Vol: 247, Pages: 525-536, ISSN: 0306-2619
Smart hybrid heat pumps have the capability to perform smart switching between electricity and gas by employing a fully-optimized control technology with predictive demand-side management to automatically use the most cost-effective heating mode across time. This enables a mechanism for delivering flexible demand-side response in a domestic setting. This paper conducts a comprehensive analysis of the fine-grained data collected during the world’s first sizable field trial of smart hybrid heat pumps to present the benefits of the smart control technology. More specifically, a novel flexibility quantification framework is proposed to estimate the capability of heat pump demand shifting based on preheating. Within the proposed framework, accurate estimation of baseline heat demand during the days with interventions is fundamentally critical for understanding the effectiveness of smart control. Furthermore, diversity of heat pump demand is quantified across different numbers of households as an important input into electricity distribution network planning. Finally, the observed values of the Coefficient of Performance (COP) have been analyzed to demonstrate that the smart control can optimize the heat pump operation while taking into account a variety of parameters including the heat pump output water temperature, therefore delivering higher average COP values by maximizing the operating efficiency of the heat pump. Finally, the results of the whole-system assessment of smart hybrid heat pumps demonstrate that the system value of smart control is between 2.1 and 5.3 £ bn/year.
Sun M, Zhang T, Wang Y, et al., 2019, Using Bayesian deep learning to capture uncertainty for residential net load forecasting, IEEE Transactions on Power Systems, ISSN: 0885-8950
Decarbonization of electricity systems drives significant and continued investments in distributed energy sources to support the cost-effective transition to low-carbon energy systems. However, the rapid integration of distributed photovoltaic (PV) generation presents great challenges in obtaining reliable and secure grid operations because of its limited visibility and intermittent nature. Under this reality, net load forecasting is facing unprecedented difficulty in answering the following question: how can we accurately predict the net load while capturing the massive uncertainties arising from distributed PV generation and load, especially in the context of high PV penetration? This paper proposes a novel probabilistic day-ahead net load forecasting method to capture both epistemic uncertainty and aleatoric uncertainty using Bayesian deep learning, which is a new field that combines Bayesian probability theory and deep learning. The proposed methodological framework employs clustering in subprofiles and considers residential rooftop PV outputs as input features to enhance the performance of aggregated net load forecasting. Numerical experiments have been carried out based on fine-grained smart meter data from the Australian grid with separately recorded measurements of rooftop PV generation and loads. The results demonstrate the superior performance of the proposed scheme compared with a series of state-of-theart methods and indicate the importance and effectiveness of subprofile clustering and high PV visibility.
Oulis Rousis A, Konstantelos I, Strbac G, 2019, A planning model for a hybrid AC/DC microgrid using a novel GA/AC OPF algorithm, IEEE Transactions on Power Systems, ISSN: 0885-8950
This paper focuses on developing an appropriate combinatorial optimization technique for solving the optimal sizing problem of hybrid AC/DC microgrids. A novel two-stage iterative approach is proposed. In the first stage, a metaheuristic technique based on a tailor-made genetic algorithm is used to tackle the optimal sizing problem, while, in the second, a non-linear solver is deployed to solve the operational problem subject to the obtained design/investment decisions. The proposed approach, being able to capture technical characteristics such as voltage and frequency through a detailed power flow algorithm, provides accurate solutions and therefore can address operational challenges of microgrids. Its capability to additionally capture contingencies ensures that the proposed sizing solutions are suitable both during normal operation and transient states. Finally, the genetic algorithm provides convergence of the model with relative computational simplicity. The proposed model is applied to a generalizable microgrid comprising of AC and DC generators and loads, as well as various types of storage technologies in order to demonstrate the benefits. The load and natural resources data correspond to real data.
Takis-Defteraios G, Papadaskalopoulos D, Ye Y, et al., Role of Flexible Demand in Supporting Market-Based Integration of Renewable Generation, 13th IEEE PES PowerTech Conference, Publisher: IEEE
Previous work has analyzed the renewable generation hosting capacity of electricity systems and the relevant value of flexible demand from a techno-economic perspective, considering the balancing and network challenges associated with a large-scale integration of renewables. This paper investigates these issues from a market perspective, considering the challenges of low energy prices and renewables’ investment cost recovery. In this context, a multi-period bi-level optimization model is developed, where the upper level maximizes the renewable generation capacity subject to the long-term profitability constraint and the lower level represents the market clearing process, accounting for the time-coupling operational constraints of flexible demand. This bi-level problem is solved after converting it to a single-level mixed-integer linear problem (MILP). Case studies validate the proposed model and demonstrate that demand flexibility increases the maximum renewable generation capacity that can be integrated in the system without violating its profitability constraint.
Cremer J, Konstantelos I, Strbac G, From optimization-based machine learning to interpretable security rules for operation, IEEE Transactions on Power Systems, ISSN: 0885-8950
Various supervised machine learning approaches have been used in the past to assess the power system security (also known as reliability). This is typically done by training a classifier on a large number of operating points whose post-fault status (stable or unstable) has been determined via time-domain simulations. The output of this training process can be expressed as a security rule that is used online to classify an operating point. A critical, and little-studied aspect of these approaches is the interpretability of the rules produced. The lack of interpretability is a well-known issue of some machine learning approaches, especially when dealing with difficult classification problems. In the case of the security assessment of the power system, which is a complex mission-critical task, interpretability is a key requirement for the adoption and deployment by operators ofthese approaches.In this paper, for the first time, we explore the trade-offbetween predictive accuracy and interpretability in the contextof power system security assessment. We begin by demonstratinghow Decision Trees (DTs) can be used to learn data-driven security rules and use the tree depth as a measure for interpretability.We leverage disjunctive programming to formulate novel training methods, capable of learning high-quality DTs while stillmaintaining interpretability. In particular, we propose two newapproaches: (i) Optimal Classification Trees (OCT∗) is proposedfor training DTs of low-depth and (ii) Greedy Optimizationbased Tree (GOT) is proposed for training DTs of intermediate depth, where the increased computational burden is managed by exploiting the nested tree structure. We also demonstrate that the ability to generate high-quality interpretable rules can actually translate to impressive benefits in terms of training requirements. Through case studies on the IEEE 68-bus system, we demonstrate that the proposed methods can produce DTs of higher quality compared to the state-
Oderinwale T, Ye Y, Papadaskalopoulos D, et al., Impact of energy storage on market-based generation investment planning, 13th IEEE PES PowerTech Conference Milano 2019, Publisher: IEEE
Previous work has analyzed the role of energy storage (ES) on generation investment planning through centralised cost-minimization models which are inherited from the era of regulated electricity utilities. This paper investigates this issue in the context of the deregulated market environment by proposing a new strategic generation investment planning model. The decision making of a strategic generation company is modeled through a multi-period bi-level optimization problem, where the upper level determines the profit-maximizinginvestment decisions of the generation company and the lower level represents themarket clearing process, accounting for the time-coupling operational characteristics of ES. This bi-level problem is solved after converting it to a single-level mixed-integer linear problem (MILP). Case studies demonstrate thatthe introduction of ES reduces the total generation capacity investment and enhances investments in “must-run” baseload generation over flexible peaking generation, yielding significant system cost savings.
Badesa L, Teng F, Strbac G, Simultaneous scheduling of multiple frequency services in stochastic unit commitment, IEEE Transactions on Power Systems, ISSN: 0885-8950
The reduced level of system inertia in low-carbon power grids increases the need for alternative frequency services. However, simultaneously optimising the provision of these services in the scheduling process, subject to significant uncertainty, is a complex task given the challenge of linking the steady-state optimisation with frequency dynamics. This paper proposes a novel frequency-constrained Stochastic Unit Commitment (SUC) model which, for the first time, co-optimises energy production along with the provision of synchronised and synthetic inertia, Enhanced Frequency Response (EFR), Primary Frequency Response (PFR) and a dynamically-reduced largest power infeed. The contribution of load damping is modelled through a linear inner approximation. The effectiveness of the proposed model is demonstrated through several case studies for Great Britain’s 2030 power system, which highlight the synergies and conflicts among alternative frequency services, as well as the significant economic savings and carbon reduction achieved by simultaneously optimising all these services.
Trovato V, Sanz IM, Chaudhuri B, et al., 2019, Preventing cascading tripping of distributed generators during non-islanding conditions using thermostatic loads, INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS, Vol: 106, Pages: 183-191, ISSN: 0142-0615
Strbac G, Pudjianto D, Aunedi M, et al., 2019, Cost-effective decarbonization in a decentralized market the benefits of using flexible technologies and resources, IEEE Power and Energy Magazine, Vol: 17, Pages: 25-36, ISSN: 1540-7977
Qadrdan M, Fazeli R, Jenkins N, et al., 2019, Gas and electricity supply implications of decarbonising heat sector in GB, ENERGY, Vol: 169, Pages: 50-60, ISSN: 0360-5442
Sun M, Wang Y, Strbac G, et al., 2019, Probabilistic peak load estimation in smart cities using smart meter data, IEEE Transactions on Industrial Electronics, Vol: 66, Pages: 1608-1618, ISSN: 0278-0046
Adequate capacity planning of substationsand feeders primarily depends on an accurate estimationof the future peak electricity demand. Traditional coinci-dent peak demand estimation is carried out based on theempirical metric, after diversity maximum demand (ADMD),indicating individual peak consumption levels and of de-mand diversification across multiple residents. With theprivilege of smart meters in smart cities, this paper pro-poses a data-driven probabilistic peak demand estima-tion framework using fine-grained smart meter data andsocio-demographic data of the consumers, which drivefundamental electricity consumptions across different cat-egories. In particular, four main stages are integrated inthe proposed approach: load modeling and sampling viathe proposed variable truncated R-vine copulas (VTRC)method; correlation-based customer grouping; probabilis-tic normalized maximum diversified demand (NMDD) esti-mation; and probabilistic peak demand estimation for newcustomers. Numerical experiments have been conductedon real demand measurements across 2,639 households inLondon, collected from Low Carbon London (LCL) projectssmart-metering trial. The mean absolute percentage error(MAPE) and pinball loss function are used to quantitativelydemonstrate the superiority of the proposed approach interms of the point estimate value and the probabilisticresult, respectively.
Oulis Rousis A, Konstantelos I, Fatouros P, et al., 2019, An AC OPF with voltage – frequency coupling constraints for addressing operational challenges of AC/DC microgrids, REM2018: Renewable Energy Integration with Mini/Microgrid, Publisher: Elsevier, Pages: 261-266, ISSN: 1876-6102
This paper focuses on developing an appropriate optimization technique for solving the optimal operation problem of hybrid AC/DC microgrids. A non-linear mathematical formulation is deployed to solve the problem subject to the exhaustive set of constraints and equations pertaining to the operation of AC and DC networks. The proposed approach, being able to capture technical characteristics, such as voltage and frequency, through the detailed power flow algorithm, provides accurate solutions and therefore can address operational challenges of MGs. The approach is applied to a highly-generalizable microgrid comprising of AC and DC generators and loads, as well as storage technologies in order to demonstrate the benefits. The simulation results demonstrate how voltage and frequency are effectively captured across the whole network via the utilised formulation and the power flow through the interlinking converter is associated with frequency (i.e. 49-51 Hz) and voltage variation (i.e. 0.95-1.05 p.u.).
Sun M, Wang Y, Teng F, et al., 2019, Clustering-based residential baseline estimation: a probabilistic perspective, IEEE Transactions on Smart Grid, ISSN: 1949-3061
Demand Response (DR) is one of the most cost-effective solutions for providing flexibility to power systems. The extensive deployment of DR trials and the roll-out of smart meters enable the quantification of consumer responsiveness to price signals via baseline estimation. The traditional deterministic baseline estimation approach can provide only a single value without consideration of uncertainty. This paper proposes a novel probabilistic baseline estimation framework that consists of a daily load profile pool construction stage, a deep learning-based clustering stage, an optimal cluster selection stage, and a quantile regression forests model construction stage. In particular, the concept of a daily load profile pool is introduced, and a deep-learning-based clustering approach is employed to handle a large number of daily patterns to further improve the baseline estimation performance. Case studies have been conducted on fine-grained smart meter data collected from a real dynamic time-of-use (dTOU) tariffs trial of the Low Carbon London (LCL) project. The superior performance of the proposed method is demonstrated based on a series of evaluation metrics regarding both deterministic and probabilistic estimation results.
De Paola A, Fele F, Angeli D, et al., 2019, Distributed coordination of price-responsive electric loads: a receding horizon approach, 57th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 6033-6040, ISSN: 0743-1546
This paper presents a novel receding horizon framework for the power scheduling of flexible electric loads performing heterogeneous periodic tasks. The loads are characterized as price-responsive agents and their interactions are modelled through an infinite-time horizon aggregative game. A distributed control strategy based on iterative better-response updates is proposed to coordinate the loads, proving its convergence and global optimality with Lyapunov stability tools. Robustness with respect to variations in the number and tasks of players is also ensured. Finally, the performance of the control scheme is evaluated in simulation, coordinating the daily battery charging of a large fleet of electric vehicles.
Sun M, Teng F, Zhang X, et al., 2019, Data-driven representative day selection for investment decisions: a cost-oriented approach, IEEE Transactions on Power Systems, Vol: 34, Pages: 2925-2936, ISSN: 0885-8950
Power system investment planning problems become intractable due to the vast variability that characterizes system operation and the increasing complexity of the optimization model to capture the characteristics of renewable energy sources (RES). In this context, making optimal investment decisions by considering every operating period is unrealistic and inefficient. The conventional solution to address this computational issue is to select a limited number of representative operating periods by clustering the input demand-generation patterns while preserving the key statistical features of the original population. However, for an investment model that contains highly complex nonlinear relationship between input data and optimal investment decisions, selecting representative periods by relying on only input data becomes inefficient. This paper proposes a novel investment costoriented representative day selection framework for large scale multi-spacial investment problems, which performs clustering directly based on the investment decisions for each generation technology at each location associated with each individual day. Additionally, dimensionality reduction is performed to ensure that the proposed method is feasible for large-scale power systems and high-resolution input data. The superior performance of the proposed method is demonstrated through a series of case studies with different levels of modeling complexity.
Hussain A, Rousis AO, Konstantelos I, et al., 2019, Impact of uncertainties on resilient operation of microgrids: A data-driven approach, IEEE Access, Vol: 7, Pages: 14924-14937, ISSN: 2169-3536
In this paper, the impact of uncertainties in loads, renewable generation, market price signals, and event occurrence time on the feasible islanding and survivability of microgrids is analyzed. A data-driven approach is proposed for estimating the maximum deviation level of uncertain parameters dynamically based on historical data. Similarly, fragility curves are utilized for determining the preparation time for the potential events based on the estimated event occurrence time and physical constraints of the microgrid components. In addition, a resilience-oriented demand response program is proposed for enhancing the utilization of renewables and other available resources for reducing the load shedding during the emergency period. Finally, a resilience index is proposed for quantifying the benefits of the proposed method for the resilience-oriented operation of microgrids. In normal mode, the impact of event occurrence time and uncertainty level is analyzed via an adaptive robust optimization method. In emergency mode, 10 000 Monte Carlo scenarios of all the uncertain parameters are generated, and their impact on the operation cost, amount of load shed, and the range of the proposed resilience index are analyzed for each case.
Sun M, Strbac G, Djapic P, et al., 2019, Preheating quantification for smart hybrid heat pumps considering uncertainty, IEEE Transactions on Industrial Informatics, ISSN: 1551-3203
The deployment of smart hybrid heat pumps can introduce considerable benefits to electricity systems via smart switching between electricity and gas while minimizing the total heating cost for each individual customer. In particular, the fully-optimized control technology can provide flexible heat that redistributes the heat demand across time for improving the utilization of low-carbon generation and enhancing the overall energy efficiency of the heating system. To this end, accurate quantification of preheating is of great importance to characterize the flexible heat. This paper proposes a novel data-driven preheating quantification method to estimate the capability of heat pump demand shifting and isolate the effect of interventions. Varieties of fine-grained data from a real-world trial are exploited to estimate the baseline heat demand using Bayesian deep learning while jointly considering epistemic and aleatoric uncertainties. A comprehensive range of case studies are carried out to demonstrate the superior performance of the proposed quantification method and then, the estimated demand shift is used as an input into the whole-system model to investigate the system implications and quantify the range of benefits of rolling-out the smart hybrid heat pumps developed by PassivSystems to the future GB electricity systems.
Cremer J, Konstantelos I, Tindemans S, et al., 2019, Data-driven power system operation: Exploring the balance between cost and risk, IEEE Transactions on Power Systems, Vol: 34, Pages: 791-801, ISSN: 0885-8950
Supervised machine learning has been successfully used in the past to infer a system's security boundary by training classifiers (also referred to as security rules) on a large number of simulated operating conditions. Although significant research has been carried out on using classifiers for the detection of critical operating points, using classifiers for the subsequent identification of suitable preventive/corrective control actions remains underdeveloped. This paper focuses on addressing the challenges that arise when utilizing security rules for control purposes. The inherent trade-off between operating cost and security risk is explored in detail. To optimally navigate this trade-off, a novel approach is proposed that uses an ensemble learning method (AdaBoost) to infer a probabilistic description of a system's security boundary and Platt Calibration to correct the introduced bias. Subsequently, a general-purpose framework for building probabilistic and disjunctive security rules of a system's secure operating domain is developed that can be embedded within classic operation formulations. Through case studies on the IEEE 39-bus system, it is showcased how security rules can be efficiently utilized to optimally operate the system under multiple uncertainties while respecting a user-defined cost-risk balance. This is a fundamental step towards embedding data-driven models within classic optimisation approaches.
Lee H, Byeon G-S, Jeon J-H, et al., 2019, An Energy Management System With Optimum Reserve Power Procurement Function for Microgrid Resilience Improvement, IEEE ACCESS, Vol: 7, Pages: 42577-42585, ISSN: 2169-3536
Zhang X, Strbac G, Shah N, et al., 2019, Whole-system assessment of the benefits of integrated electricity and heat system, IEEE Transactions on Smart Grid, Vol: 10, Pages: 1132-1145, ISSN: 1949-3061
The interaction between electricity and heat systems will play an important role in facilitating the cost effective transition to a low carbon energy system with high penetration of renewable generation. This paper presents a novel integrated electricity and heat system model in which, for the first time, operation and investment timescales are considered while covering both the local district and national level infrastructures. This model is applied to optimize decarbonization strategies of the UK integrated electricity and heat system, while quantifying the benefits of the interactions across the whole multi-energy system, and revealing the trade-offs between portfolios of (a) low carbon generation technologies (renewable energy, nuclear, CCS) and (b) district heating systems based on heat networks (HN) and distributed heating based on end-use heating technologies. Overall, the proposed modeling demonstrates that the integration of the heat and electricity system (when compared with the decoupled approach) can bring significant benefits by increasing the investment in the heating infrastructure in order to enhance the system flexibility that in turn can deliver larger cost savings in the electricity system, thus meeting the carbon target at a lower whole-system cost.
Konstantelos I, Jamgotchian G, Tindemans S, et al., 2018, Implementation of a Massively Parallel Dynamic Security Assessment Platform for Large-Scale Grids, IEEE-Power-and-Energy-Society General Meeting (PESGM), Publisher: IEEE, ISSN: 1944-9925
Rousis AO, Chairiman, Pipelzadeh Y, et al., 2018, Voltage Support from Distribution Level Resources in South-East England, IEEE-Power-and-Energy-Society General Meeting (PESGM), Publisher: IEEE, ISSN: 1944-9925
Pipelzadeh Y, Moreno R, Chaudhuri B, et al., 2018, Corrective Control With Transient Assistive Measures: Value Assessment for Great Britain Transmission System, IEEE-Power-and-Energy-Society General Meeting (PESGM), Publisher: IEEE, ISSN: 1944-9925
Gong X, De Paola A, Angeli D, et al., 2018, A Distributed Price-based Strategy for Flexible Demand Coordination in Multi-area, IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe), Publisher: IEEE, ISSN: 2165-4816
Greve T, Teng F, Pollitt MG, et al., 2018, A system operator's utility function for the frequency response market, Applied Energy, Vol: 231, Pages: 562-569, ISSN: 0306-2619
How can the electricity system operator determine the optimal quantity and quality of electricity ancillary services (such as frequency response) to procure in a market increasingly characterized by intermittent renewable electricity generation? The paper presents a system operator’s utility function to calculate the exchange rates in monetary values between different frequency response products in the electricity system. We then use the utility function in a two-sided Vickrey-Clarke-Groves (VCG) mechanism combined of two frequency response products – enhanced and primary – in the context of the system in Great Britain. This mechanism would allow the market to reveal to the system operator the welfare optimal mix of speed of frequency response and quantity to procure. We show that this mechanism is the efficient way to support new faster sources of frequency response, such as could be provided by grid scale batteries.
de Paola A, Angeli D, Strbac G, 2018, On distributed scheduling of flexible demand and Nash equilibria in the electricity market, Dynamic Games and Applications, Vol: 8, Pages: 761-798, ISSN: 2153-0785
This paper presents a novel game theory approach for large-scale deployment of price-responsive electrical appliances. In the proposed distributed control scheme, each appliance independently schedules its power consumption on the basis of a broadcast demand/price signal, aiming to complete its task at minimum cost. The conflicting interactions of the appliances, competing for power consumption at the cheapest hours of the day, are modelled through a differential game with a continuum of players, and efficient deployment of flexible demand is characterized as a Nash equilibrium. A novel approach is adopted to derive necessary and sufficient equilibrium conditions: intrinsic properties of the problem (price monotonicity, unidirectionality of power transfers) are exploited to perform an equilibrium study based on sublevel sets of the considered demand profiles. As a result, it is possible to determine for which penetration levels of flexible demand, types of appliances and inflexible demand profiles it is possible to achieve an equilibrium. Such stable configuration is achieved through the broadcast of a single demand/price signal and does not require iterated exchange of information between devices and coordinator. In addition, the global optimality of the equilibrium is proved, necessary conditions for Pareto optimality are derived, and a preliminary analysis of devices with partial time availability is carried out. The performance of the proposed control strategy is evaluated in simulation, considering realistic future scenarios of the UK power system with large penetration of flexible demand.
Ye Y, Papadaskalopoulos D, Moreira R, et al., Investigating the Impacts of Price-Taking and Price-Making Energy Storage in Electricity Markets through an Equilibrium Programming Model, IET Generation, Transmission & Distribution
Papadaskalopoulos D, Moreira R, Strbac G, et al., 2018, Quantifying the potential economic benefits of flexible industrial demand in the European power system, IEEE Transactions on Industrial Informatics, Vol: 14, Pages: 5123-5132, ISSN: 1551-3203
The envisaged decarbonization of the European power system introduces complex techno-economic challenges to its operation and development. Demand flexibility can significantly contribute in addressing these challenges and enable a cost-effective transition to the low-carbon future. Although extensive previous work has analyzed the impacts of residential and commercial demand flexibility, the respective potential of the industrial sector has not yet been thoroughly investigated despite its large size. This paper presents a novel, whole-system modeling framework to comprehensively quantify the potential economic benefits of flexible industrial demand (FID) for the European power system. This framework considers generation, transmission and distribution sectors of the system, and determines the least-cost long-term investment and short-term operation decisions. FID is represented through a generic, process-agnostic model, which however accounts for fixed energy requirements and load recovery effects associated with industrial processes. The numerical studies demonstrate multiple significant value streams of FID in Europe, including capital cost savings by avoiding investments in additional generation and transmission capacity and distribution reinforcements, as well as operating cost savings by enabling higher utilization of renewable generation sources and providing balancing services.
De Paola A, Gong X, Angeli D, et al., 2018, Coordination of micro-storage devices in power grids: a multi-agent system approach for energy arbitrage, IEEE Conference on Control Technology and Applications (CCTA), Publisher: IEEE, Pages: 871-878
Sun M, Cremer J, Strbac G, 2018, A novel data-driven scenario generation framework for transmission expansion planning with high renewable energy penetration, Applied Energy, Vol: 228, Pages: 546-555, ISSN: 0306-2619
Transmission expansion planning (TEP) is facing unprecedented challenges with the rise of integrated renewable energy resources (RES), flexible load elements, and the potential electrification of transport and heat sectors. Under this reality, the inadequate information of the stochastic parameters’ behavior may lead to inefficient expansion decisions, especially in the context of very high renewable penetration. This paper proposes a novel data-driven scenario generation framework for the TEP problem to generate unseen but important load and wind power scenarios while capturing inter-spatial dependencies between loads and wind generation units’ output in various locations, using a vine-copula based high-dimensional stochastic variable modeling approach. The superior performance of the proposed model is demonstrated through a case study on a modified IEEE 118-bus system. The expected result of using the expected value problem solution (EEV) and the net benefits of transmission expansion (NBTE) are used as the evaluation metrics to quantitatively illustrate the advantages of the proposed approach. In addition, the case of very high wind penetration is carried out to further highlight the importance of the multivariate stochastic dependence of load and wind power generation. The results demonstrate that the proposed scenario generation method can result in near-optimal investment decisions for the TEP problem that make more net benefits than using limited number of historical data.
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