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  • 1.
    Ahmed, Kazi Main Uddin
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math H. J.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    A Novel Reliability Index to Assess the Computational Resource Adequacy in Data Centers2021In: IEEE Access, E-ISSN 2169-3536, Vol. 9, p. 54530-54541Article in journal (Refereed)
    Abstract [en]

    The energy demand of data centers is increasing globally with the increasing demand for computational resources to ensure the quality of services. It is important to quantify the required resources to comply with the computational workloads at the rack-level. In this paper, a novel reliability index called loss of workload probability is presented to quantify the rack-level computational resource adequacy. The index defines the right-sizing of the rack-level computational resources that comply with the computational workloads, and the desired reliability level of the data center investor. The outage probability of the power supply units and the workload duration curve of servers are analyzed to define the loss of workload probability. The workload duration curve of the rack, hence, the power consumption of the servers is modeled as a function of server workloads. The server workloads are taken from a publicly available data set published by Google. The power consumption models of the major components of the internal power supply system are also presented which shows the power loss of the power distribution unit is the highest compared to the other components in the internal power supply system. The proposed reliability index and the power loss analysis could be used for rack-level computational resources expansion planning and ensures energy-efficient operation of the data center.

  • 2.
    Ahmed, Kazi Main Uddin
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math H. J.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Characterizing Failure and Repair Time of Servers in a Hyper-scale Data Center2020In: Proceedings of 2020 IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe) 26-28 October, 2020, IEEE, 2020, p. 660-664Conference paper (Refereed)
    Abstract [en]

    Hyper-scale data centers are used to host cloud computing interfaces to support the increasing demand for storage and computational resources. For achieving specific service level agreements (SLA), this infrastructure demands highly available cloud computing systems. It is necessary to analyze the server failure incidents to determine the way of improving the reliability of the system since the computational interruption causes financial losses for the data center owners. Regarding the reliability analysis, it is important to characterize the time to failure and time to repair of the servers. In this paper, a publicly available data set from Google cloud-cluster data center will be analyzed to find the distribution function for the time to failure and the time to repair for the servers in a cloud based data centers.

  • 3.
    Ahmed, Kazi Main Uddin
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math H.J.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Reliability Analysis of Internal Power Supply Architecture of Data Centers in Terms of Power Losses2021In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 193, article id 107025Article in journal (Refereed)
    Abstract [en]

    The number of data centers and the energy demand are increasing globally with the development of information and communication technology (ICT). The data center operators are facing challenges to limit the internal power losses and the unexpected outages of the computational resources or servers. The power losses of the internal power supply system (IPSS) increase with the increasing number of servers that causes power supply capacity shortage for the devices in IPSS. The aim of this paper is to address the outage probability of the computational resources or servers due to the power supply capacity shortage of the power distribution units (PDUs) in the IPSS. The servers outage probability at rack-level defines the service availability of the data center since the servers are the main computational resource of it. The overall availability of the IPSS and the power consumption models of the IPSS devices are also presented in this paper. Quantitative studies are performed to show the impacts of the power losses on the service availability and the overall availability of the IPSS for two different IPSS architectures, which are equivalent to the Tier I and Tier IV models of the data center.

  • 4.
    Ahmed, Kazi Main Uddin
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math H. J.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Letha, Shimi Sudha
    Electrical Engineering, National Institute of Technical Teachers, Chandigarh, India.
    The Impacts of Voltage Disturbances Due to Faults In the Power Supply System of A Data Center2022In: 2022 20th International Conference on Harmonics & Quality of Power (ICHQP) Proceedings: “Power Quality in the Energy Transition”, IEEE, 2022Conference paper (Refereed)
    Abstract [en]

    The internal power condition system (IPCS) in data centers is prone to have cable faults that cause voltage dips and swells. The voltage dips and swells impact the power supply units (PSUs) with the servers. The servers connected with the PUSs restart or turn-off when the input voltage comes out of the voltage-tolerance range. This paper analyses the impact of such voltage disturbances on server outages due to a single-phase fault in the IPCS. The voltage-tolerance range of the PSUs is considered according to the guideline of the Information Technology Industry Council (ITIC). The voltage dip propagates to the healthy load sections from the fault location, while voltage swells are also observed due to sudden load reduction. Moreover, the current limitation mode of the inverter in the uninterrupted power supply (UPS) is identified as a cause of voltage dip to almost zero experienced by the PSUs. The reliability of the data center considering the outage probability of the servers are finally quantified to show the impacts of the voltage dips and swells in the IPCS.

  • 5.
    Ahmed, Kazi Main Uddin
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math H.J
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    A Review of Data Centers Energy Consumption And Reliability Modeling2021In: IEEE Access, E-ISSN 2169-3536, Vol. 9, article id 152536Article, review/survey (Refereed)
    Abstract [en]

    Enhancing the efficiency and the reliability of the data center are the technical challenges for maintaining the quality of services for the end-users in the data center operation. The energy consumption models of the data center components are pivotal for ensuring the optimal design of the internal facilities and limiting the energy consumption of the data center. The reliability modeling of the data center is also important since the end-user’s satisfaction depends on the availability of the data center services. In this review, the state-of-the-art and the research gaps of data center energy consumption and reliability modeling are identified, which could be beneficial for future research on data center design, planning, and operation. The energy consumption models of the data center components in major load sections i.e., information technology (IT), internal power conditioning system (IPCS), and cooling load section are systematically reviewed and classified, which reveals the advantages and disadvantages of the models for different applications. Based on this analysis and related findings it is concluded that the availability of the model parameters and variables are more important than the accuracy, and the energy consumption models are often necessary for data center reliability studies. Additionally, the lack of research on the IPCS consumption modeling is identified, while the IPCS power losses could cause reliability issues and should be considered with importance for designing the data center. The absence of a review on data center reliability analysis is identified that leads this paper to review the data center reliability assessment aspects, which is needed for ensuring the adaptation of new technologies and equipment in the data center. The state-of-the-art of the reliability indices, reliability models, and methodologies are systematically reviewed in this paper for the first time, where the methodologies are divided into two groups i.e., analytical and simulation-based approaches. There is a lack of research on the data center cooling section reliability analysis and the data center components’ failure data, which are identified as research gaps. In addition, the dependency of different load sections for reliability analysis of the data center is also included that shows the service reliability of the data center is impacted by the IPCS and the cooling section.

  • 6.
    Ahmed, Kazi Main Uddin
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    de Oliveira, Roger Alves
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Risk Assessment of Server Outages Due To Voltage Dips In the Internal Power Supply System of a Data Center2021In: CIRED 2021 - The 26th International Conference and Exhibition on Electricity Distribution, Institution of Engineering and Technology, 2021, p. 708-712, article id 0090Conference paper (Refereed)
    Abstract [en]

    The data centers host sensitive electronic devices like servers, memory, hard disks, network devices, etc., which are supplied by the power supply units. The regulated direct current (DC) output of the power supply units fluctuates with input voltage variation since they typically contain single phase switch-mode power supplies. The voltage dips caused by faults in the internal power supply system of the data center can be large enough to violate the Information Technology Industry Council (ITIC) proposed voltage-tolerance guideline. The output of the power supplies, hence the operation of the servers will be interrupted due to such voltage dips. In this paper, the outage probability of the servers caused by the voltage dips are analyzed for different fault location in the internal supply system of a data center.

  • 7.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Distribution Network Planning Considering Capacity Mechanisms and Flexibility2019Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The increasing penetration of distributed energy resources (DERs) has posed challenges to the distribution system operator (DSO) from the operation and regulatory point of view. High penetration of DERs could have negative impacts on the performance of the distribution grid, and depending on the regulatory framework, the DSO's remuneration as well. In liberalized electrical systems, the focus on promoting eciency has led to the implementation of an incentive-based regulation that exerts additional pressure on the DSOs to reduce costs. Additionally, the European Parliament Directive 2009/72/EC establishes a regulatory unbundling among the distribution, production, and retailing activities within the same vertically integrated electric utility.

    A way of helping the DSO to cope with the posed challenges is by providing it with exibility. This exibility can be acquired from the planning stage, and later be used during the system operation. This exibility can stem from the DSO's ability to exert control on the demand and the supply side to balance the system and correct its operational state.

    Based on the European DSOs' current situation at facing the increasing penetration of DERs, this thesis investigates in non-wired exible grid tools to solve the distribution network expansion problem. The investigation focuses on exibility providers, in particular on energy storage systems and hydropower, and also on capacity mechanisms to translate the capacity from DERs into the grid's capacity for planning purposes.

    Given that the share of renewable sources among the DERs is increasing, and considering the importance of energy storage systems in providing exibility to balance renewable energy production, the eort has been turned on to developing a hydropower model and a generic storage model that t both planning and operational studies.

    Given the need for gearing the DERs' behavior into the DSO's decision making process during the planning and operational timescales, the design and implementation of a distribution capacity mechanism have been developed. The design of the capacity mechanism has been conceived considering its integration within the distribution network expansion problem.

    The outcomes of this thesis can be synthesized as follows: 1) A generic hydraulic/storage model provided with an equivalent marginal cost that aids in considering the impact of present decisions in the future costs. 2) A market oriented distribution capacity mechanism that gears DERs and the DSOs to benefit mutually. 3) A distribution network expansion planning formulation that integrates the capacity resource from DERs through the distribution capacity mechanism.

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  • 8.
    Alvarez, Manuel
    et al.
    Universidad Simón Bolívar, Caracas.
    Bermúdez, Juan
    Universidad Simón Bolívar, Caracas.
    Marginal pricing via penalty factors in the Venezuelan hydrothermal system2006In: 2006 IEEE PES Transmission and Distribution Conference and Exposition: Latin America, TDC'06, Piscataway, NJ: IEEE Communications Society, 2006, article id 4104756Conference paper (Refereed)
    Abstract [en]

    The work shown next deals with the definition of nodal marginal prices, in the context of an economic dispatch solution with transmission losses. The losses are incorporated through penalty factors obtained from line distribution factors, using a linearization process. This study is applied to the hydrothermal venezuelan system, considering plants with regulation capability and run-of-river dams. The objective function to be minimized includes present and future thermal costs. In addition, a discussion is given about the correct location of the slack node, in order to get similar results to these associated to an OPF solution. © 2006 IEEE.

  • 9.
    Alvarez, Manuel
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Rönnberg, Sarah
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Zhong, Jin
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Gil-de-Castro, Aurora
    University of Cordoba, Electronics and Electronic Technology Area, University of Cordoba.
    A Smart Distribution Toolbox for Distribution System Planning2015Conference paper (Refereed)
    Abstract [en]

    The distribution system planner should be able to coordinate smart grid solutions in order to find cost effective expansions plans. These plans should be able to deal with new added system uncertainties from renewable production and consumers while guaranteeing power quality and availability of supply. This paper proposes a structure for distribution systems planning oriented to help the planner in deciding how to make use of smart solutions for achieving the described task. Here, the concept of a system planning toolbox is introduced and supported with a review of relevant works implementing smart solutions. These are colligated in a way that the system planner can foresee what to expect with their combined implementation. Future developments in this subject should attempt to theorize a practical algorithm in an optimization and decision making context.

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  • 10.
    Alvarez, Manuel
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Rönnberg, Sarah
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Frías, Pablo
    Comillas Pontifical University, Madrid, Spain.
    Cossent, Rafael
    Comillas Pontifical University, Madrid, Spain.
    Jabr, Rabih
    American University of Beirut, Beirut, Lebanon.
    Zhong, Jin
    The University of Hong Kong, Hong Kong, China.
    A Capacity Mechanism Design for Distribution Network Expansion Planning2018In: 2018 IEEE International Conference on Environment and Electrical Engineering and 2018 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe), 2018, article id 8493874Conference paper (Refereed)
    Abstract [en]

    Capacity remuneration mechanisms have been originally oriented to ensure availability and continuity of supply on the power generation pool. Equivalent generation-based capacity mechanisms could be implemented to enhance and prolong the usability of the distribution grid. In particular, such capacity mechanisms would provide an alternative to traditional expansion options leading to investment deferral. In this work, a distribution capacity mechanism to fit within a distribution network planning methodology will be proposed and discussed. The capacity mechanism will be outlined following similar guidelines as for the design of capacity mechanisms used in the energy only market. The result of the design is a volume based capacity auction for a capacity-constrained system, oriented to both the active and the reactive power provision.

  • 11.
    Alvarez Perez, Manuel Alejandro
    Luleå University of Technology, Department of Engineering Sciences and Mathematics.
    Stochastic Planning of Smart Electricity Distribution Networks2017Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    The penetration of intermittent Distributed Generation (DG) brought additional uncertainty to the system operation and planning. To cope with uncertainties the Distribution System Operator (DSO) could implement several strategies. These strategies range from the inclusion of smart technologies which will increment system’s flexibility and resiliency, to improvements in forecasting, modeling, and regulatory pledge that will facilitate the planning activity. Regardless of the nature of the solutions, they could be collected in a sort of toolbox. The planner will access the toolbox to conform cost effective plans, better able to deal with any uncertainty. The present work will address the problem of distribution system planning under uncertainties, considering smart solutions along with traditional reinforcements, in the short-term lead time up to 3 years ahead. The work will be focused on three aspects that are the cornerstones of this work:

     • A planning facilitating strategy: Distribution Capacity Contracts (DCCs).

     • A flexibility enabler technology: Energy Storage.

     • A binding methodology: Multistage Stochastic Programming. Stochastic dual dynamic programming (SDDP). 

    Under the present directive of the European Parliament concerning common rules for the internal market in electricity, distribution companies are not allowed to own DG but entitled to include it as a planning option to differ investment in traditional grid reinforcements. An evaluation of the regulatory context will lead this work to consider DCCs as a planning alternative available in the toolbox. The impact of this type of contract on the remuneration of the DG owner will be assessed in order to provide insight on its willingness to participate. The DCCs might aid the DSO to defer grid i ii investments during planning stages and to control the network flows during operation. 

    Given that storage solutions help to match in time production from intermittent sources with load consumption, they will play a major role in dealing with uncertainties. A generic storage model (GSM) based on a future cost piecewise approximation will be developed. This model inspired by hydro-reservoirs will help assessing the impact of storage in planning decisions. This model will be tested by implementing it in short-term hydro scheduling and unit commitment studies. 

    To trace a path towards the future of this research work, a discussion on the planning problem formulation, under consideration of the lead time, the expansion options, the smart strategies, and the regulatory framework will be presented. Special focus will be given to multistage stochastic programming methods and in particular to the SDDP approach.

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  • 12.
    Alvarez Perez, Manuel Alejandro
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Rönnberg, Sarah
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bermúdez, Juan
    Universidad Simón Bolívar.
    Zhong, Jin
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science. The University of Hong Kong.
    Bollen, Math
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    A Generic Storage Model Based on a Future Cost Piecewise-Linear Approximation2019In: IEEE Transactions on Smart Grid, ISSN 1949-3053, E-ISSN 1949-3061, Vol. 10, no 1, p. 878-888Article in journal (Refereed)
    Abstract [en]

    This work presents a generic storage model (GSM) inspired by the scheduling of hydraulic reservoirs. The model for steady state short-term (ST) operational studies interlaces with the long-term (LT) energy scheduling through a piecewise-linear Future Cost Function (FCF). Under the assumption that a Stochastic Dual Dynamic Programming (SDDP) approach has been used to solve the energy schedule for the LT, the FCF output from that study will be processed to obtain an equivalent marginal opportunity cost for the storage unit. The linear characteristic of a segment of the future cost function (FCF) will allow a linear modeling of the storage unit production cost. This formulation will help to coordinate the renewable resource along with storage facilities in order to find the optimal operation cost while meeting end-point conditions for the long-term plan of the energy storage. The generic model will be implemented to represent a battery storage and a pumped-hydro storage. A stochastic unit commitment (SUC) with the GSM will be formulated and tested to assess the day-ahead scheduling strategy of a Virtual Power Plant (VPP) facing uncertainties from production, consumption, and market prices.

  • 13.
    Alvarez Perez, Manuel Alejandro
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Rönnberg, Sarah
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bermúdez, Juan
    Universidad Simón Bolívar.
    Zhong, Jin
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    A Hydro-Reservoir Generic Storage Model for Short-Term Hydrothermal Coordination2017In: IEEE PES PowerTech Manchester 2017: towards and beyond sustainable energy systems, 2017, Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2017, article id 7980882Conference paper (Refereed)
    Abstract [en]

    This work presents a linear solution for the short-term hydro-thermal scheduling problem linked to long-term conditions through a piecewise-linear Future Cost Function (FCF). Given end-point conditions to conform long-term water releases, and given actual reservoir conditions, a segment of a pre-built piecewise future cost function will be chosen. The linear characteristic of the FCF segment will allow a linear modeling of the hydro-power plant, in a similar fashion as a thermal unit with an equivalent marginal opportunity cost. A short-term hydro thermal coordination problem will be formulated considering parallel and cascaded hydro-reservoirs. Three study cases involving different reservoir configurations and scenarios will be computed to test the model. The results of this model mimics coherently the future-cost hydro-thermal coordination problem for the different configurations tested. Given similarities with other forms of energy storage, a new theoretical model for generic storage will be proposed and discussed.

  • 14.
    Alvarez Perez, Manuel Alejandro
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Rönnberg, Sarah
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bermúdez, Juan
    Department of Energy Conversion and Transport, Simón Bolívar University.
    Zhong, Jin
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Reservoir-Type Hydropower Equivalent Model Based on a Future Cost Piecewise Approximation2018In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 155, p. 184-195Article in journal (Refereed)
    Abstract [en]

    The long-term (LT) scheduling of reservoir-type hydropower plants is a multistage stochastic dynamic problem that has been traditionally solved using the stochastic dual dynamic programming (SDDP) approach. This LT schedule of releases should be met through short-term (ST) scheduling decisions obtained from a hydro-thermal scheduling that considers uncertainties. Both time scales can be linked if the ST problem considers as input the future cost function (FCF) obtained from LT studies. Known the piecewise-linear FCF, the hydro-scheduling can be solved as a one-stage problem. Under certain considerations a single segment of the FCF can be used to solve the schedule. From this formulation an equivalent model for the hydropower plant can be derived and used in ST studies. This model behaves accordingly to LT conditions to be met, and provides a marginal cost for dispatching the plant. A generation company (GENCO) owning a mix of hydro, wind, and thermal power will be the subject of study where the model will be implemented. The GENCO faces the problem of scheduling the hydraulic resource under uncertainties from e.g. wind and load while determining the market bids that maximize its profit under uncertainties from market prices. A two-stage stochastic unit commitment (SUC) for the ST scheduling implementing the equivalent hydro model will be solved.

  • 15.
    Alvarez Perez, Manuel Alejandro
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Rönnberg, Sarah
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Cossent, Rafael
    Universidad Pontificia de Comillas.
    Zhong, Jin
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Regulatory Matters Affecting Distribution Planning With Distributed Generation2017In: CIRED - Open Access Proceedings Journal, E-ISSN 2515-0855, Vol. 2017, no 1, p. 2869-2873Article in journal (Refereed)
    Abstract [en]

    Under the present European directive concerning common rules for the internal market in electricity, distribution companies are not allowed to own distributed generation (DG) but encouraged to include it as a planning option to defer investment in traditional grid reinforcements. Distribution system operators (DSOs) have used the provision of capacity contracted to DG as a viable alternative under current regulatory arrangements. Here, the topics bonding DSOs and DG owners under the present regulation will be explored and a planning structure that considers distribution capacity contracts as a planning option will be proposed. This will serve as a road map for DSOs to implement its preferred planning tools in an optimisation context, considering costs of investment, reliability, operation, and capacity provision while complying with current regulation.

  • 16.
    Alvarez Perez, Manuel Alejandro
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Rönnberg, Sarah
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Cossent, Rafael
    Universidad Pontificia de Comillas.
    Zhong, Jin
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Remuneration Assessment of a VPP Providing Distribution Capacity Services2017In: IEEE PES PowerTech Manchester 2017: towards and beyond sustainable energy systems, Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2017, article id 7980881Conference paper (Refereed)
    Abstract [en]

    A Distribution System Operator (DSO) might consider a capacity contract as a planning alternative to defer grid investments. A Virtual Power Plant (VPP) might be able to provide such capacity and change its production as requested by the DSO. This article presents an assessment of the impact of this type of distribution capacity contract (DCC) on VPP's remuneration. This assessment is done by comparing the optimal production / bidding strategy which maximize its profit, under presence or absence of these contracts. The impact of intermittent generation and storage while evaluating these scenarios will be investigated as well. A stochastic unit commitment will be used to determine the VPP's strategy under uncertainties from wind power, load, market prices, and the requested power by the DSO. The model showed that the VPP involvement in distribution capacity contracts can improve its remuneration when certain types of Distributed Energy Resources (DER) are used to provide the service.

  • 17.
    Avila-Rojas, A. E.
    et al.
    Department of Electrical and Electronic Engineering, Los Andes University, Bogotá, Colombia.
    De Oliveira-De Jesus, P. M.
    Department of Electrical and Electronic Engineering, Los Andes University, Bogotá, Colombia.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Distribution network electric vehicle hosting capacity enhancement using an optimal power flow formulation2022In: Electrical engineering (Berlin. Print), ISSN 0948-7921, E-ISSN 1432-0487, Vol. 104, no 3, p. 1337-1348Article in journal (Refereed)
    Abstract [en]

    This paper presents a method based on an optimal power flow (OPF) procedure to determine the maximum Hosting Capacity (HC) of Electric Vehicles (EV) that can be supported by a distribution network. With a focus on the injection control of reactive power, it is possible to maximize the penetration of EV. The presented method is based on linearized power flow equations, allowing a significant reduction in the computational processing times. Two comparisons are presented. The first one is between a nonlinear and a linear OPF method. Second one, it is comparative analysis between legacy iterative (non-optimized) method of HC and the proposed method. The method is applied on the IEEE 13 node test feeder circuit showing its effectiveness and acceptable performance. Results demonstrate that the implemented method enhances the HC measured against a legacy HC method and decrease the computational time measures against nonlinear optimization methods. 

  • 18.
    Bakhtiari, Hamed
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Zhong, Jin
    University of Hong Kong, Hong Kong.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Predicting the stochastic behavior of uncertainty sources in planning a stand-alone renewable energy-based microgrid using Metropolis–coupled Markov chain Monte Carlo simulation2021In: Applied Energy, ISSN 0306-2619, E-ISSN 1872-9118, Vol. 290, article id 116719Article in journal (Refereed)
    Abstract [en]

    Due to the lack of available flexibility sources to cope with different uncertainties in the real-time operation of stand-alone renewable energy-based microgrids, the stochastic behavior of uncertainty sources needs to be included in the planning stage. Since there is a high association between some of the uncertainty sources, defining a proper time series to represent the behavior of each source of uncertainty is a challenging issue. Consequently, uncertainty sources should be modeled in such a way that the designed microgrid be able to cope with all scenarios from probability and impact viewpoints. This paper proposes a modified Metropolis–coupled Markov chain Monte Carlo (MC)3 simulation to predict the stochastic behavior of different uncertainty sources in the planning of a stand-alone renewable energy-based microgrid. Solar radiation, wind speed, the water flow of a river, load consumption, and electricity price have been considered as primary sources of uncertainty. A novel data classification method is introduced within the (MC)3 simulation to model the time-dependency and the association between different uncertainty sources. Moreover, a novel curve-fitting approach is proposed to improve the accuracy of representing the multimodal distribution functions, modeling the Markov chain states, and the long-term probability of uncertainty sources. The predicted representative time series with the proposed modified (MC)3 model is benchmarked against the retrospective model, the long-term historical data, and the simple Monte Carlo simulation model to capture the stochastic behavior of uncertainty sources. The results show that the proposed model represents the probability distribution function of each source of uncertainty, the continuity of samples, time dependency, the association between different uncertainty sources, short-term and long-term trends, and the seasonality of uncertainty sources. Finally, results confirm that the proposed modified (MC)3 can appropriately predict all scenarios with high probability and impact.

  • 19.
    Bakhtiari, Hamed
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Zhong, Jin
    University of Hong Kong, Hong Kong.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Risk-Averse Pricing Strategy for Demand ResponseManuscript (preprint) (Other academic)
    Abstract [en]

    Interruptible/curtailable demand response program (ICDRP) is a valuable ancillary service resource in electricity markets. Due to the uncertainty of customer behavior in a market, risk-based pricing for ICDRP is needed. It is also necessary to evaluate the eligibility conditions for utilizing uncertain ICDRP as an ancillary service. In this paper, we first propose a pricing strategy that allocates payoffs to the coalition of ICDRP participants considering risk management costs caused by the uncertain responsiveness of ICDRP participants while maximizing the system operator’s ability to cope with uncertainties and optimizing generation outputs and regulation price in the frequency regulation market. Then, we investigate the flexibility of predetermined reserves in the forward electricity market as an eligibility condition for risk-averse utilization of ICDRP. A risk-averse Shapley value method is developed in the proposed pricing strategy. Finally, we carry out numerical studies to illustrate the feasibility and effectiveness of the proposed pricing strategy to determine the incentives and penalties in a fair way. We also demonstrate the necessity of considering the uncertainties of ICDRP responsiveness in the required reserve selection process to successfully exploit the benefits of ICDRP in the frequency regulation market.

  • 20.
    Bakhtiari, Hamed
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Zhong, Jin
    The University of Hong Kong, Hong Kong.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    The Utilization of Demand Response Programs In Renewable-based Microgrids: Benefits and Challenges2021In: CIRED 2021 - The 26th International Conference and Exhibition on Electricity Distribution, Institution of Engineering and Technology, 2021, p. 2999-3003, article id 0213Conference paper (Refereed)
  • 21.
    Bakhtiari, Hamed
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Zhong, Jin
    University of Hong Kong, Hong Kong.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Uncertainty modeling methods for risk-averse planning and operation of stand-alone renewable energy-based microgrids2022In: Renewable energy, ISSN 0960-1481, E-ISSN 1879-0682, Vol. 199, p. 866-880Article in journal (Refereed)
    Abstract [en]

    The accuracy of models to capture the uncertainty of renewables significantly affects the planning and operation of renewable energy-based stand-alone (REB-SA) microgrids. This paper aims to first study different stochastic and deterministic models for renewables, then evaluate the performance of an REB-SA microgrid planning problem and provide qualitative and quantitative comparisons. A modified Metropolis-coupled Markov chain Monte Carlo simulation is considered for the first time in the planning of an REB-SA microgrid to predict the behavior of renewables with minimum iterations. The modified model is benchmarked against two prevalent models including the retrospective model with worst-case scenarios and the Monte Carlo simulation. The operations of three designed microgrids (by these three methods) are evaluated using the last three-year historical data of a city in northern Sweden including solar radiation, wind speed, the water flow of a river, and load consumption. The impacts of the considered methods on using PV panels and hydrogen systems are investigated. The results verify that the modified model decreases the risk of planning and operation of an REB-SA microgrid from the energy and power shortage viewpoints. Moreover, the designed microgrid with the modified model can cope with all possible scenarios from economic, technical, and environmental viewpoints.

  • 22.
    Bermúdez, Juan
    et al.
    Universidad Simón Bolívar.
    Alvarez, Manuel
    Universidad Simón Bolívar, Caracas.
    Inclusion of ancillary services in a cost-based centralized economic dispatch solution for hydrothermal systems2007In: LESCOPE'07: 2007 Large Engineering Systems Conference on Power Engineering : conference proceedings : the Delta Centre-Ville Hotel, Montreal, Quebec, Canada, October 10-12, 2007, Piscataway, NJ: IEEE Communications Society, 2007, p. 131-136, article id 4437366Conference paper (Refereed)
    Abstract [en]

    In this paper a centralized economic dispatch is developed, where some services are included, associated to frequency control and generation outages. The study can consider thermal machines but hydro turbines as well, both of the run-of-river or regulation type, in whose case the objective function is the present and future thermal cost in the context of the stochastic dual dynamic programming (SDDP), simplified for academic purposes [8][6]. In this study the immediate plus future thermal cost is minimized, taking into account the primary reserves requirement in each unit (speed governor primary action), plus the AGC reserve, besides the (tertiary) reserves, associated to the outage of any turbine (n-1 criterion). The problem proposed was resolved using a linear programming commercial package. For the sake of clarifying the results, some didactical cases are solved, where comparisons are discussed between the traditional energy-only dispatch and the model herein proposed. This paper extends in a very simple manner the results of a traditional cost-based centralized economic dispatch, of the hydrothermal case, to include the AGC restrictions and spinning reserves requirements. © 2007 IEEE.

  • 23.
    Bermúdez, Juan
    et al.
    Universidad Simón Bolívar.
    Alvarez, Manuel
    Universidad Simón Bolívar.
    Villasana, R.
    Universidad Simón Bolívar.
    Khodr, H. M.
    GECAD–Knowledge Engineering and Decision-Support Research Group of the Electrical Engineering Institute of Porto.
    Una metodologia para combinar los manteniminentos forzados y preventivos en etapas de panficacion2009Conference paper (Refereed)
    Abstract [en]

    El Mantenimiento Correctivo (MC) o forzado es clásicamente un evento de naturaleza aleatoria,pero el Mantenimiento Preventivo (MP) o programado puede ser considerado un eventodeterminístico. Ahora bien, estrictamente hablando es imposible predecir cuándo exactamente unequipo será parado por efectos de MP, ni cuánto tiempo durará en ese estado. Por ende, a pesar decualquier programación que pueda realizarse, el MP es en realidad un evento aleatorio, cuyostiempos de permanencia en cada uno de sus vertientes (equipo operativo / equipo no operativo),pueden considerarse exponencialmente distribuidos, si el equipo está dentro de su periodo de deVida Útil. De ser así, la teoría de Markov puede ser utilizada para definir una forma de combinarlos dos procesos aleatorios, a nivel de la tasa de fallas y la duración de las paradas para cadaequipo, para posteriormente extender la aplicación a sistemas complejos, con generación ytransmisión considerados simultáneamente.En este trabajo se desarrolla tal esquema, el cual una vez formulado es aplicado a cálculostradicionales de confiabilidad en sistemas de potencia, tales como LOLE, ELOL, Elementos enSerie/Paralelo y Conjuntos de Corte. Se hacen comparaciones con las consideracionesdeterminísticas tradicionales, que sirvan para ilustrar las bondades de la metodología propuesta.Obviamente esta metodología se adapta perfectamente a las modernas simulaciones de MonteCarlo.

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  • 24.
    Bermúdez, Juan
    et al.
    Universidad Simón Bolívar.
    Leanez, F.
    Pontificia Universidad Católica de Chile.
    Alvarez, Manuel
    Universidad Simón Bolívar, Caracas.
    Khodr, H. M.
    GECAD - Knowledge Engineering and Decision-Support Research Center.
    A generalized methodology based on symmetrical components for multiple-fault calculation in power systems2009In: Electric power components and systems, ISSN 1532-5008, E-ISSN 1532-5016, Vol. 37, no 10, p. 1081-1101Article in journal (Refereed)
    Abstract [en]

    This article presents an efficient computational method to solve the problem of simultaneous multiple faults in power systems, using a conventional symmetrical component formulation. The methodology made possible the development of a programming routine, which takes into account a generic set of boundary conditions for almost any type of fault or combination of faults that can occur simultaneously, involving any number of phases. The program was tested with IEEE 14-, 57-, 118-, and 300-busbar benchmark systems facing up to ten simultaneous series and shunt faults. The results were satisfactorily tested against classical three-phase formulation solutions.

  • 25.
    Castro, Guillermo
    et al.
    Inelectra, Caracas.
    Bermúdez, Juan
    Universidad Simón Bolívar, Caracas.
    Jimenez, Manuel
    Universidad Simón Bolívar, Caracas.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Arreaza, Alex
    Derwick Associates of Venezuela.
    AVRs and PSSs Revisited2015In: 2015 9th International Conference on Electrical and Electronics Engineering: ELECO 2015, Bursa, Turkey, 26 - 28 November 2015, Piscataway, NJ: IEEE Communications Society, 2015, p. 1006-1010, article id 7394473Conference paper (Refereed)
    Abstract [en]

    In this paper a conceptual analysis on the effect ofAutomatic Voltage Regulators (AVR) and Power SystemStabilizers (PSS) for small signal stability (SSS) of powersystems is developed. A modal formulation approachincluding the use of the Participation Matrix is used. TheModal Formulation is performed considering synchronousgenerator (SG) equations for both the Electromotive Forces(EMF) model and the Flux Linkages (FL) model as well asAVR and PSS equations. Then, a selected study case isevaluated to study the effect of the AVR and PSS on thesmall signal stability. For pedagogical purposes acomparison between the basic RLC circuit and asynchronous generator connected to an infinite bus, toclarify the concepts of synchronizing torque and dampingtorque, is presented.1. Introduction

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  • 26. De Oliveira-De Jesus, P. M.
    et al.
    Alvarez, Manuel
    Universidad Simón Bolívar, Caracas.
    Ponce de Leao, M. T.
    Yusta, J. M.
    University of Zaragoza.
    Uncertainty Assessment of Incremental Transmission Loss Factors2008In: Power systems and power technology: proceedings of the 8th WSEAS International Conference on Power Systems (PS 2008) ; Santander, Cantabria, Spain, September 23 - 25, 2008 / [ed] José Ma. Zamanillo Sáinz de la Maza, WSEAS Press , 2008, p. 195-200Conference paper (Refereed)
  • 27.
    De Oliveira-De Jesus, P. M.
    et al.
    Universidad Simón Bolívar.
    Alvarez, Manuel
    Universidad Simón Bolívar, Caracas.
    Ponce de Leao, M. T.
    DEEC-FEUP Oporto.
    Yusta, JM
    Universidad de Zaragoza.
    A Novel Approach to Evaluate Incremental Transmission Losses2009In: WSEAS Transactions on Power Systems, Vol. 4, no 1, p. 12-21Article in journal (Refereed)
    Abstract [en]

    During the past thirty years, the evaluation of incremental losses in transmission systems has beenwidespread around the world encompassing a fundamental task in order to solve the well-known economic dispatchproblem. Nowadays, incremental losses or computation of penalty factors has gained a new relevance allocatingtransmission losses among market participants being integrated in the spot pricing model. Nevertheless, vagueness in power injections from load demand and renewable resources has a fundamental influence on transmission incremental losses, and consequently affecting spot prices of the energy. This paper presents a new method to compute Incremental Transmission Loss (ITL) factors taking into account the effect of uncertainty on power injections due to measurement errors or future estimation. Fuzzy Set Theory is applied to deal with vagueness of information about power injections. The proposed technique provides a broad spectrum of feasibility of incremental losses in order to perform operational planning tasks by Transmission System Operators or network regulators. A 3-bus system is used to illustrate the proposed methodology.

  • 28.
    Jesus, P. M. De Oliveira-De
    et al.
    Energy Institute and Department of Conversion and Energy Delivery, Simon Bolivar University, Caracas.
    Alvarez, Manuel
    Energy Institute and Department of Conversion and Energy Delivery, Simon Bolivar University, Caracas.
    Yusta, J. M.
    Department of Electrical Engineering, University of Zaragoza.
    Distribution power flow method based on a real quasi-symmetric matrix2013In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 95, p. 148-159Article in journal (Refereed)
    Abstract [en]

    This paper presents a new load flow formulation to solve active and passive electric distribution networks. The fundamental idea discussed here is how to obtain the power flow solution by using the elements of a unique quasi-symmetric matrix called TRX in the iterative process. The method is formulated for single-phase balanced and three-phase unbalanced radially operated networks. It works with real variables as opposed to complex variables used in previous backward/forward sweep algorithms discussed in literature. The proposed TRX matrix constitutes a complete database by including information of network topology structure as well as branch impedances of the distribution feeder. Data arrangement is suitable to be exchanged under standard Common Information Model (CIM) under Distribution Management Systems (DMS) environment allowing an efficient computation of the state of the system for on-line and off-line study applications. The proposed methodology was applied on a group of IEEE test systems and a real distribution system of 49,000 nodes. © 2012 Elsevier B.V. All rights reserved.

  • 29.
    Mousavi, Milad
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    A contract-based trading of power flexibility between a variable renewable energy producer and an electricity retailer2023In: Sustainable Energy, Grids and Networks, ISSN 2352-4677, Vol. 34, article id 101067Article in journal (Refereed)
    Abstract [en]

    Variable renewable energy producers and electricity retailers encounter several uncertainties in their decision-making problems, such as intermittency of renewable energy sources, variability of consumption, and market price volatility. To cope with these uncertainties, this paper presents a new contract-based trading mechanism of power flexibility (FlexCon) between two parties, a variable renewable energy producer and an electricity retailer. The proposed mechanism is managed by a new entity, named FlexCon operator, to oversee the energy and financial trades through the contract and coordinate the transactions with the system operator. Through the FlexCon, the parties are able to exchange their energy imbalances as a source of power flexibility to alleviate the negative impacts of uncertainties in their decision-making problems. To this end, two two-stage stochastic linear problems are introduced from each party’s point of view. In the first stage, the variable renewable energy producer and the electricity retailer submit their bids to sell and purchase in the day-ahead market, respectively. Following the day-ahead market clearing, closer to the delivery time, the parties submit their decisions on the contract to the introduced FlexCon operator. The operator allocates possible power flexibility transactions based on the surpluses or shortages of the parties. Assuming that the imbalances are not completely resolved with the FlexCon, the remaining deviations are settled in the balancing market. The parties’ decisions related to the balancing market and the FlexCon are modeled in the second stage of the stochastic problem. The uncertainties associated with prices, renewable generation, electricity consumption, and the maximum exchangeable power flexibility through the FlexCon are considered via scenarios. Meanwhile, the profit risk is considered by the Conditional Value at Risk measure. The numerical results show that FlexCon effectively diminishes the impacts of uncertainties on the parties’ profit.

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  • 30.
    Mousavi, Milad
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Zhong, Jin
    University of Hong Kong, China.
    A review on local flexibility market advancements: practices in Nordic countries2023In: 27th International Conference on Electricity Distribution (CIRED 2023), Institution of Engineering and Technology, 2023, p. 3816-3820, article id 1394Conference paper (Refereed)
    Abstract [en]

    This paper surveys the most recent local flexibility markets (LFMs) initiatives in three Nordic countries: Finland, Norway, and Sweden. First, the significant distinctions in flexibility needs in the region are identified and analyzed. Then, considering the recently practiced LFMs in these countries, a review of their aims, description, and implementation is performed. Moreover, their key findings and future research directions are discussed. The LFM platforms evaluated in this review are EU-SysFlex, INTERRFACE, NODES, DRES2Market, CoordiNet, SthlmFlex, and InterFlex. The analyses assert that the new LFM models express a promising technical and economic vision for increasing flexibility from the costumers' and aggregators' side by delivering grid and system services for both transmission system operators (TSOs) and distribution system operators (DSOs) in a coordinated context.

  • 31.
    Piemonti, Carlos
    et al.
    Universidad Simón Bolívar, Caracas.
    Bermúdez, Juan
    Universidad Simón Bolívar.
    Khodr, H. M.
    Universidad Simón Bolívar, Caracas.
    Alvarez, Manuel
    Universidad Simón Bolívar, Caracas.
    Optimal solutions for the Venezuelan unit commitment hydrothermal system2006In: 2006 IEEE PES Transmission and Distribution Conference and Exposition: Latin America, TDC'06, Piscataway, NJ: IEEE Communications Society, 2006, article id 4104749Conference paper (Refereed)
    Abstract [en]

    This work is about different optimal solutions for the unit commitment problem in the Venezuelan hydrothermal power system, disregarding the transmission system. The centralized cost-based maximum net social benefit solution, the oligopoly solution and the unregulated monopoly solution are formulated and analyzed. The oligopoly is studied via Nash-Cournot equilibrium, obtained iteratively considering both price-maker and price-taker firms. The price-demand curves are created using a price-demand elasticity parameter. The hydro plants can be of the run-of-river type or can have a regulation period, like in the case of Guri. In latter case the future profit is represented by a fixed volume of water to be turbined in the day ahead. Since integer variable are necessary to simulate the shut-down, start-up process a mixed integer commercial programming application is employed. © 2006 IEEE.

  • 32.
    Sorrentino, Elmer
    et al.
    Universidad Simón Bolívar, Caracas.
    Alvarez, Manuel
    Universidad Simón Bolívar, Caracas.
    Análisis de la Curva de Daño de Transformadores para Varias Conexiones Usadas en Sistemas de Distribución2010Conference paper (Refereed)
    Abstract [en]

    Resumen—Se presenta un análisis de las curvas de daño de lostransformadores de distribución para las siguientes conexiones:a) monofásica, con toma central en el secundario; b) estrellaabierta-delta abierta, con o sin toma central en una rama de ladelta secundaria; c) delta abierta-delta abierta, con o sin tomacentral en una rama de la delta secundaria; d) estrella-delta,con toma central en una rama de la delta secundaria, con o sinpuesta a tierra del neutro de la estrella primaria; e) delta-delta,con toma central en una rama de la delta secundaria. Para cadauno de los casos se obtuvo el factor por el cual hay quemultiplicar las corrientes con el fin de trasladarhorizontalmente la curva de daño del transformador. Dichofactor es necesario para verificar si la protección primariaefectivamente protege al equipo. Además, se analizó el efecto deemplear transformadores monofásicos de distinta capacidad.

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  • 33.
    Sorrentino, Elmer
    et al.
    Universidad Simón Bolívar, Caracas.
    Alvarez, Manuel
    Universidad Simón Bolívar, Caracas.
    Multipliers to shift the through-fault protection curve for various connections of distribution transformers2011In: IEEE Transactions on Power Delivery, ISSN 0885-8977, E-ISSN 1937-4208, Vol. 26, no 3, p. 2055-2057, article id 5725148Article in journal (Refereed)
    Abstract [en]

    This paper presents the multipliers to shift the through-fault protection curve for various connections of distribution transformers. Cases with a secondary center tap and with secondary open delta were analyzed as well as the effect of using single-phase units with different short-circuit impedances. © 2011 IEEE.

  • 34.
    Uddin Ahmed, Kazi Main
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Bollen, Math H. J.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    Alvarez, Manuel
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.
    A Stochastic Approach to Determine the Optimal Number of Servers for Reliable and Energy Efficient Operation of Data Centers2023In: IEEE Transactions on Sustainable Computing, E-ISSN 2377-3782, Vol. 8, no 2, p. 153-164Article in journal (Refereed)
    Abstract [en]

    The increasing demand of the data center's computational capacity in recent years has introduced new data center operational challenges among others to maintain the service level agreements (SLA) and quality of services (QoS), while at the same time limiting energy consumption. In this paper, a stochastic operational risk assessment approach is presented that estimates the required number of spare servers in a data center considering the risk of servers' failure in operation since servers define the computational capability of a data center. A reliability index called “risk of computational resource commitment (RCRC)” is introduced that quantifies the probability of having insufficient spare servers due to failures during the operational lead time, and the complement of the RCRC shows the ability of the resources to maintain SLA of a data center. The failure rates of the servers are obtained using a Monte Carlo Simulation with the failure data, published by Google in 2019. The analysis shows that the RCRC reduces with the increasing number of spare servers, while it also stresses the energy efficiency of the data center. The RCRC index could be used in data center operation to avoid overprovisioning of the servers and to limit the number of spare servers in the data center, while creating a suitable balance between QoS and energy consumption of the data centers.

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