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Assistsant professor with Faculty of Electrical Engineering in Bialystok University of Technology, Poland. Since 2015 Head of Laboratory of alternative electric power sources. Reviewer of many manuscripts submitted to well recognizable international journals. Research interests: application of a few classes of stochastic processes, probabilistic logic and Bayesian networks in analytic and simulation modeling of: (i) reliability of power systems with wind power sources interconnected to, (ii) output power of correlated wind turbines (and wind farms), (iii) short- and mid-term output power prediction, (iv) decision processes of wind turbines maintenance planning (v) reliability of internal collection grids of onshore and offshore wind farms
Because of the stochastic nature of wind turbines, the output power management of wind power generation (WPG) is a fundamental challenge for the integration of wind energy systems into either power systems or microgrids (i.e., isolated systems consisting of local wind energy systems only) in operation and planning studies. In general, a wind energy system can refer to both one wind farm consisting of a number of wind turbines and a given number of wind farms sited at the area in question. In power systems (microgrid) planning, a WPG should be quantified for the determination of the expected power flows and the analysis of the adequacy of power generation. Concerning this operation, the WPG should be incorporated into an optimal operation decision process, as well as unit commitment and economic dispatch studies. In both cases, the probabilistic investigation of WPG leads to a multivariate uncertainty analysis problem involving correlated random variables (the output power of either wind turbines that constitute wind farm or wind farms sited at the area in question) that follow different distributions. This paper advances a multivariate model of WPG for a wind farm that relies on indexed semi-Markov chains (ISMC) to represent the output power of each wind energy system in question and a copula function to reproduce the spatial dependencies of the energy systems’ output power. The ISMC model can reproduce long-term memory effects in the temporal dependence of turbine power and thus understand, as distinct cases, the plethora of Markovian models. Using copula theory, we incorporate non-linear spatial dependencies into the model that go beyond linear correlations. Some copula functions that are frequently used in applications are taken into consideration in the paper; i.e., Gumbel copula, Gaussian copula, and the t-Student copula with different degrees of freedom. As a case study, we analyze a real dataset of the output powers of six wind turbines that constitute a wind farm situated in Poland. This dataset is compared with the synthetic data generated by the model thorough the calculation of three adequacy indices commonly used at the first hierarchical level of power system reliability studies; i.e., loss of load probability (LOLP), loss of load hours (LOLH) and loss of load expectation (LOLE). The results will be compared with those obtained using other models that are well known in the econometric field; i.e., vector autoregressive models (VAR).
Guglielmo D’Amico; Giovanni Masala; Filippo Petroni; Robert Adam Sobolewski. Managing Wind Power Generation via Indexed Semi-Markov Model and Copula. Energies 2020, 13, 4246 .
AMA StyleGuglielmo D’Amico, Giovanni Masala, Filippo Petroni, Robert Adam Sobolewski. Managing Wind Power Generation via Indexed Semi-Markov Model and Copula. Energies. 2020; 13 (16):4246.
Chicago/Turabian StyleGuglielmo D’Amico; Giovanni Masala; Filippo Petroni; Robert Adam Sobolewski. 2020. "Managing Wind Power Generation via Indexed Semi-Markov Model and Copula." Energies 13, no. 16: 4246.
The capacity factor (performance) of wind farms is quite unsatisfactory and is much lower as compared to conventional power generation units. The performance refers, among others, to ‘electric and electronic components’ of wind farms, i.e. generators, transformers, cables, busbars, protection systems, power electronic units, and many more. Assuring a high availability of the components can require their high both reliability and quality of preventive and corrective maintenance strategies. Reliability and maintenance of protection systems (one or more protective relays, circuit breaker, wiring, and other components) can result in major wind farms operation upsets and substantially influence their performance. Recently, microprocessor-based electronic relays have been developed and are being applied at increasing rate. They are usually equipped with self-monitoring and checking module. Some of the protection system failures can be hidden ones, i.e. to be detected: within planned maintenance, by self-monitoring and checking module or while fault or failure of protected component occurred. Availability rate can be a main criterion of system’ reliability and maintenance. It is a probability that a system occupies up state within a long time, and can be calculate relying on semi-Markov model presented in the study. One of the application of the model can be valuable feedback and recommendations on time interval of periodic planned maintenance that maximizes the system’ availability. As an example, the optimal time interval of planned maintenance along different both failure rates and probabilities of detecting the failures, is calculated relying on the model and presented in the case study.
Robert Adam Sobolewski. Probabilistic Modelling of Reliability and Maintenance of Protection Systems Incorporated into Internal Collection Grid of a Wind Farm. Advances in Intelligent Systems and Computing 2020, 585 -595.
AMA StyleRobert Adam Sobolewski. Probabilistic Modelling of Reliability and Maintenance of Protection Systems Incorporated into Internal Collection Grid of a Wind Farm. Advances in Intelligent Systems and Computing. 2020; ():585-595.
Chicago/Turabian StyleRobert Adam Sobolewski. 2020. "Probabilistic Modelling of Reliability and Maintenance of Protection Systems Incorporated into Internal Collection Grid of a Wind Farm." Advances in Intelligent Systems and Computing , no. : 585-595.
Fulfilment of reliability requirements for ‘electrical components’ of wind farm internal collection grid with combination of good wind resources assure the satisfactory performance of a farm. Concerning on-shore farm the feeder section faults lead to the loss of energy served from either all downstream turbines or all turbines in the farm. The failures of protection systems in terms of failures to trip and false tripping increase the incidence and extent the losses of energy served in greater degree as compared to other designs. Achievement of satisfactory performance (in terms of accepted amount of energy not served) in relation to reliability issues, requires the fulfilment of the reliability requirements. They should be obtained relying on quantitative reliability models and take into account: reliability parameters of the components, the topology of collection grid, quality of renewal action and false tripping of protection systems. In the paper the original approach to reliability modeling of on-shore wind farm internal collection grid is presented in details. It relies on semi-Markov model and takes into account the faults and failures of components, the combinations of the components faults and failures that lead to particular number of generators on outage, and the quality of renewal action and false tripping of protective relays. The reliability measure is expected energy not served by farm within specific period of time. The example of reliability model application is presented in details as well.
Robert Adam Sobolewski. Semi-Markov Reliability Model of Internal Electrical Collection Grid of On-Shore Wind Farm. Advances in Intelligent Systems and Computing 2019, 466 -477.
AMA StyleRobert Adam Sobolewski. Semi-Markov Reliability Model of Internal Electrical Collection Grid of On-Shore Wind Farm. Advances in Intelligent Systems and Computing. 2019; ():466-477.
Chicago/Turabian StyleRobert Adam Sobolewski. 2019. "Semi-Markov Reliability Model of Internal Electrical Collection Grid of On-Shore Wind Farm." Advances in Intelligent Systems and Computing , no. : 466-477.
The major drawback of wind energy relies in its variability in time, which necessitates specific strategies to be settled. One such strategy can be the coordination of wind power production with a co-located power generation of dispatchable energy source (DES), e.g., thermal power station, combined heat and power plant, gas turbine or compressed air energy storage. In this paper, we consider an energy producer that generates power by means of a wind park and of a DES and sells the produced energy to an isolated grid. We determine the optimal quantity of energy produced by a DES, given the unit cost of this energy, that a power producer should buy and use to hedge against the risk inherent in the production of energy through wind turbines. We determine the optimal quantity by solving a static optimization problem taking into account the possible dependence between the amount of energy produced by wind turbines and electricity prices by using a copula function. Several particular cases are studied that allow the determination of the optimal solution in an analytical closed form. Finally, a numerical example concerning a real 48 MW wind farm located in Poland and Polish Power Exchange shows the possibility of implementing the model in real-life problems.
Guglielmo D’Amico; Filippo Petroni; Robert Adam Sobolewski. Optimal Control of a Dispatchable Energy Source for Wind Energy Management. Stochastics and Quality Control 2019, 34, 19 -34.
AMA StyleGuglielmo D’Amico, Filippo Petroni, Robert Adam Sobolewski. Optimal Control of a Dispatchable Energy Source for Wind Energy Management. Stochastics and Quality Control. 2019; 34 (1):19-34.
Chicago/Turabian StyleGuglielmo D’Amico; Filippo Petroni; Robert Adam Sobolewski. 2019. "Optimal Control of a Dispatchable Energy Source for Wind Energy Management." Stochastics and Quality Control 34, no. 1: 19-34.
Performing a maintenance of wind energy system components under good wind conditions may lead to energy not served and finally – to financial losses. The best starting time of preventive maintenance will be, that reduces the energy not served in most. To find this time, a decision model is desired, where many circumstances should be taken into account, i.e. (i) the number and the order of components to be maintained, (ii) component maintenance duration, and (iii) wind turbine(s) output power prediction. Usually, preventive maintenance is planned a few days or weeks in advance. One of the decision problem representations can be influence diagram that enables choosing a decision alternative that has the lowest expected utility (energy not served). The paper presents an decision model that can support decisions-making on starting time of preventive maintenance and maintenance order of wind energy system components. The model relies on influence diagram. The conditional probability distribution of a chance nodes of the diagram are obtained relying on Bayesian networks (BN), whereas the utilities of value node in the diagram are calculated thanks to the second order semi-Markov chains (SMC). The example shows the application of the model in real case of two wind turbines located in Poland. Both the parameters of Bayesian network nodes and semi-Markov chain are derived from real data recorded by SCADA system of the both turbines and weather forecast.
Robert Adam Sobolewski; Guglielmo D’Amico; Filippo Petroni. Decision Model of Wind Turbines Maintenance Planning. Advances in Intelligent Systems and Computing 2018, 440 -450.
AMA StyleRobert Adam Sobolewski, Guglielmo D’Amico, Filippo Petroni. Decision Model of Wind Turbines Maintenance Planning. Advances in Intelligent Systems and Computing. 2018; ():440-450.
Chicago/Turabian StyleRobert Adam Sobolewski; Guglielmo D’Amico; Filippo Petroni. 2018. "Decision Model of Wind Turbines Maintenance Planning." Advances in Intelligent Systems and Computing , no. : 440-450.
Maintenance of a wind turbine is a combination of all technical, administrative and managerial actions intended to retain it in, or restore it to, a state in which the turbine is able to generate power. This paper presents an influence diagram to estimate the expected utility that represents wind turbine energy to be produced given period of time in the future. The conditional probability distribution of a chance node of the diagram is obtained relying on Bayesian networks, whereas the utilities of value node are calculated thanks to the second order semi-Markov chains. The example shows the application of the models in the real case of one wind turbine E48 by Enercon located in northern part of Poland. Both Bayesian network parameters and kernel of semi-Markov chain are derived from real data recorded by SCADA system of the turbine and weather forecast.
Guglielmo D’Amico; Filippo Petroni; Robert Adam Sobolewski; Wojciech Zamojski; Jacek Mazurkiewicz; Jarosław Sugier; Tomasz Walkowiak; Janusz Kacprzyk. Maintenance of Wind Turbine Scheduling Based on Output Power Data and Wind Forecast. Advances in Intelligent Systems and Computing 2017, 582, 106 -117.
AMA StyleGuglielmo D’Amico, Filippo Petroni, Robert Adam Sobolewski, Wojciech Zamojski, Jacek Mazurkiewicz, Jarosław Sugier, Tomasz Walkowiak, Janusz Kacprzyk. Maintenance of Wind Turbine Scheduling Based on Output Power Data and Wind Forecast. Advances in Intelligent Systems and Computing. 2017; 582 ():106-117.
Chicago/Turabian StyleGuglielmo D’Amico; Filippo Petroni; Robert Adam Sobolewski; Wojciech Zamojski; Jacek Mazurkiewicz; Jarosław Sugier; Tomasz Walkowiak; Janusz Kacprzyk. 2017. "Maintenance of Wind Turbine Scheduling Based on Output Power Data and Wind Forecast." Advances in Intelligent Systems and Computing 582, no. : 106-117.
Availability of an electrical system of a wind farm plays a crucial role among factors affecting the power output of a farm. The availability is determined by an internal collection grid topology and reliability of its components, e.g. generators, inverters, transformers, cables, switch breakers, protective relays, and busbars, to name a few. A wind farm availability’s quantitative measure can be: (i) the probability distribution of combinations of “in operation” states of the farm’s wind turbines and (ii) the expected power to be delivered to the power system. The “in operation” state of a wind turbine involves the availability of the wind turbine and other equipment necessary for the power transfer to the external grid. They can be used for the analysis of the impact of various topologies and the reliability of individual components on the availability. The second kind of analysis may be supported by the importance ranking of the components. The paper presents the approach to formulating the reliability models that is based on Bayesian networks, useful importance measures of the components and the case study that illustrates the approach application.
Robert Adam Sobolewski. Implication of Availability of an Electrical System of a Wind Farm for the Farm’s Output Power Estimation. Advances in Intelligent Systems and Computing 2016, 419 -430.
AMA StyleRobert Adam Sobolewski. Implication of Availability of an Electrical System of a Wind Farm for the Farm’s Output Power Estimation. Advances in Intelligent Systems and Computing. 2016; ():419-430.
Chicago/Turabian StyleRobert Adam Sobolewski. 2016. "Implication of Availability of an Electrical System of a Wind Farm for the Farm’s Output Power Estimation." Advances in Intelligent Systems and Computing , no. : 419-430.
Andrés Feijóo; Daniel Villanueva; José Luis Pazos; Robert Sobolewski. Simulation of correlated wind speeds: A review. Renewable and Sustainable Energy Reviews 2011, 15, 2826 -2832.
AMA StyleAndrés Feijóo, Daniel Villanueva, José Luis Pazos, Robert Sobolewski. Simulation of correlated wind speeds: A review. Renewable and Sustainable Energy Reviews. 2011; 15 (6):2826-2832.
Chicago/Turabian StyleAndrés Feijóo; Daniel Villanueva; José Luis Pazos; Robert Sobolewski. 2011. "Simulation of correlated wind speeds: A review." Renewable and Sustainable Energy Reviews 15, no. 6: 2826-2832.