Развитие методов оценки показателей балансовой надежности энергосистем с возобновляемыми источниками энергии : диссертация на соискание ученой степени кандидата технических наук : 05.14.02

Relevance of the research topic. Electric Power systems (EPSs) are undergoing a significant transformation as a result of the increasing integration of renewable energy resources, and the advent of the smart grid and its accompanying technologies. Such transformation, while it adds convenience, intelligence, and reduces environmental impacts, also adds dynamic and stochastic generations and loads that increase the systemic variability and uncertainties and so complicate the reliability assessment of EPSs. Reliability assessment has an important part in the process of adoption of EPS planning and investment [1-6]. The performance of EPS in providing adequate electric services within accepted standards to all points of consumption at any moment of time (both current and future) can be decided unacceptable or acceptable by reliability criteria [2-3, 7]. The reliability analysis approaches range from relatively simple deterministic calculations of planning reserve margins to rigorous probabilistic reliability indices [8-9].
The deterministic criterion is relatively easy to implement and interpret, but such a worst-case based deterministic approach has a main drawback in that it does not adequately reflect levels of operation risk resulted from the stochastic nature and uncertain behavior of a power system. From this perspective, probabilistic analysis methods that identify power system reliability risks needs to be investigated to better reflect the actual system behavior. This probabilistic reliability analysis incorporates the effect of uncertainties of input data on the customer service through the probabilistic evaluation of reliability indices. The probabilistic reliability indices are to identify the degree of reliability of power system through estimating the risk (probability or how likely) and the size (the expected value of frequency, duration, and magnitude) of energy deficit under a variety of scenarios. Therefore, the probabilistic methods result in effective and realistic reliability evaluation of power system. The obstacles to applying these methods are primarily computational efficiency and the lack of realistic reliability data [9]. These obstacles have been significantly overcome in recent years with the development and availability of high-
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speed computation facilities and the efforts have been dedicated to collecting the components reliability data.
After the 2003 Northeast blackout, the North American Power Reliability Corporation (NERC) and Canadian Electricity Association (CEA) have been organizing with electric utilities to collect reliability data and responsible for executing the composite power system reliability studies in North America [10-12]. CEA releases reports annually on the probabilistic analysis of transmission equipment ‘s outage performance. Also, NERC has developed the Generation Availability Data System (GADS) and the Transmission Availability Data System (TADS) to gather outage data. In industry practice, probabilistic techniques for generation adequacy analysis have been used in nearly all regions of North America to calculate the Loss of Load Expectation (LOLE) which express the planned figure of outage hours per year. The purpose is to ensure the LOLE doesn’t exceed 1 day in 10 years when all uncertainties including the forced outages of thermal generators, and renewable resources and load uncertainty are included in the simulation [13]. In Western European countries, the standard LOLE value is set at a little diverse level (3 hours per year) [14]. European Network of Electricity Transmission System Operators (ENTSO-E) annually publishes a report on the Norms, requirements, and assessment of reliability with recommendations for solving the problems of the existing methods for calculating the reliability [15]. Also, in Russia in recent years, there is an increasing interest in the problem of calculating the reliability indices. On January 1, 2019, the Preliminary National Standard of the Russian Federation was published: “304-2018: Balance reliability of power systems. Section 1. Overall regulations”, which forms the conceptual apparatus in the field of calculating the balance reliability of power systems [16]. From September 1, 2019, System Operator of the Unified Energy System introduced a technical report 59012820.27.010.005-2018 which regulates methodological instructions for carrying out calculations of balance sheet reliability [17], and from March 1, 2020, a national technical standard: “GOST R 58730-2019 Unified power system and isolated power systems. Power/Energy system planning. Balance reliability calculations. Norms and requirements” was introduced.

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With the continuous development of computational resources, tremendous amount of research has been done on developing probabilistic methods for power system reliability evaluation over the past several decades [18-54]. However, a trade- off between detailed modeling and computational cost is still an important issue, especially with the growing complexity, uncertainty, and dimensionality of a power system. A frequently adopted approach for the reliability indices assessment is the Monte Carlo simulation (MCS) due to its merits [18-20]. MCS does not impose restrictions on the form of the used distribution functions and can be used for composite system analysis when the system is highly nonlinear or has many uncertain variables. Moreover, a transfer function is not inevitably required. So, it can also be implemented in nondifferentiable as well as nonconvex problems. The price for its robustness is that MCS requires a great computational effort to guarantee the accuracy of the reliability indices results due to the MCS approach depends on sampling the whole state space of input variables, regardless where are the states that represent events of interest i.e. failure events of the power system meeting the required demand. Moreover, the high reliable property of power systems and the enlarged sample space with the probabilistic modeling of renewable energy resources and transmission lines outages increase more and more the MCS computational burden.
Researchers handled the MCS computational burden by adopting two research tracks: improvement of the state evaluation efficiency and the improvement of the sampling efficiency. The first research track is to provide high-performing programming patterns [21-35] for the purpose of spending less time in the state evaluation stage. The second track could be to develop more efficient sampling means [36-50] for focusing the sampling attempt in the regions of concern or approximate analytical methods [52-54] for representing the continuous random variables by a small number of the states required to be estimated. With the high reliable property of power systems, the improvement of the sampling efficiency is the best mean since the improvement of the state evaluation efficiency actually does not pay off without a good sampling algorithm. Thus, more efficient sampling techniques or approximate

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analytical methods for dominating the calculation burden of the MCS method are addressed in this dissertation.
The degree of scientific elaboration of the problem. A large literature, both scientific papers and technical reports, is available about power system reliability assessment and management. Considerable studies accounted for 29% articles have been addressed the computational efficiency of the probabilistic evaluation of power system reliability [55]. Rresearch on the probabilistic reliability assessment did not stop and continue until the present time. Among Russian publications, one should especially highlight the works of such scientists as: F.L. Byk, N.I. Voropai, M.A. Dubitsky, V.Yu. Itkin, V.G. Kitushin, G.F. Kovalev, Yu.N. Kucherov, L.M. Lebedeva, N.A. Manov, V.A. Nepomniachtchi, V.P. Oboskalov, M.N. Rozanov, Yu.N. Rudenko, I.A. Ushakov, G.A. Fedotova, M.B. Cheltsov, Yu. Chukreev, M. Yu. Chukreev, V.D. Shlimovich and others. The world school of reliability is mainly represented by such researchers as: R. Allan, R. Billinton, B. Borkowska, Yi Gao, J. Endrenyi, and others. In addition, there exist research groups formed within the Institute of Electrical and Electronics Engineers (IEEE) and the International Council on Large Electrical Systems (CIGRE) and other organizations, such as NERC, ENTSO-E and the Council of European Energy Regulators (CEER). Among the organizations that participated in the comparison of methods for calculating the reliability, algorithms and programs when used as a test, the scheme developed at the Siberian Power Institute (named after L.A. Melentieva), included: Siberian Power Engineering Institute named after L.A. L. A. Melentieva (software systems Yantar, Potok); Department of Energy Cybernetics of the Academy of Sciences of Moldova (software package, Composition); Komi Scientific Center of the Ural Branch of the Russian Academy of Sciences (software package, Orion) and others [56].
The purpose of the dissertation research is to develop computationally more efficient probabilistic means than the MCS method for assessing the reliability of power systems with conserving the high computation accuracy of the MCS method.

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This purpose has been declaimed to diverse degrees in the publications and the chapters on which the dissertation is based.
The objectives of the dissertation research.
• Reviewing the probabilistic approaches employed to reliability assessment of the power systems to deduce their shortcomings and so seek for an alternative approach based on developing enhancement to existing methods or a totally new method.
• Proposing probabilistic techniques with the following features: low computational time and good degree of accuracy compared with the MCS method.
• Evaluating the effectiveness of approximate analytical methods in calculating the probabilistic reliability indices.
• Developing an efficient sampling technique for focusing the sampling in the domains of interest in which loss of loads occurred to avoid the surplus time associated with the evaluation of states that make no contribution to the reliability indices.
• Studying the problem of modelling accurately based on real historical data the uncertainties of electricity demand and weather variables and representing the correlation that exists among them in a probabilistic model.
• Evaluating efficiently annual reliability indices of composite power system with renewable energy integrated (wind- solar) considering the stochastic characteristics of electricity demand and renewable energy resources.
The object of the research includes a concentrated EPS and a composite power system with limited capacities of transmission lines and concentrated EPS as separate nodes.
Scientific novelty of the dissertation research:
• The proposition of new approach based on the cross entropy-based importance sampling (CE-IS) in order to improve the sampling efficiency and convergence characteristics of the MCS method. The statistical characterization of the new approach- named ECE-IS is presented. The ECE-IS based optimization algorithm

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is more efficient and robust in sampling most states that are important to the estimators of the reliability indices than other discussed methods in literature. From the reported results, the proposed method contributes to accurately evaluating the reliability indices and further enhancing the convergence of the indices in comparison with other methods. Moreover, a great speed-up was shown in terms of computation time with respect to the standard MCS method. By reducing the number of samples required for the simulation and so enabling more time to be exhausted on evaluating each sample, the proposed method paves the way for further complete model of the EPS and so obtaining highly realistic and accurate reliability indices.
• In the case of renewable energy reliability studies, a new approach combines the ECE-IS for extracting the loss of load events and the multivariate Gaussian mixture model (MGMM) for estimating the joint probability distribution of the random variables (demand and weather variables) based on real historical data to include the load and solar and wind power uncertainties and the dependence relationships among them in the reliability assessment of EPSs. The ECE-IS approach is proposed for approximating accurately the optimal ISD of the obtained MGMM and so assist IS in sampling the region of interest for the system reliability indicators (i.e., the region in which the weather variables have lower values and electricity demand has higher value). Using the ECE-IS makes the load loss events more likely to be drawn and allows us to enlarge the sample space with the probabilistic state modeling of the renewable energy conversion systems (wind turbine generators and photovoltaic arrays) and the transmission system. Based on the author’s knowledge, no work considers all these RVs in the reliability assessment problem that develop more accurate estimates of the annual reliability indices.
The theoretical significance of the work lies in the development of alternative computationally efficient methods based on developing enhancement to previously methods or a wholly new method for probabilistic assessment of the reliability indices

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with the purpose of striking a compromise between the detailed modelling of power system uncertainties and the computational burden of reliability indices.
The practical significance of the work. With the increasing robustness of EPSs, the occurrence of loss of load events is becoming rarer. For example, the LOLP in a real power system does not exceed 0.0001. This means that the power deficit is observed, on average, no more than 0.876 hours per year. However, sequence of rare loss of load events could lead to large blackout in a power system. Therefore, all possible combinations of rare loss of load events must be sampling efficiently. This is achieved by developing the efficient rare events simulation method (ECE-IS) for defining the approximately optimal ISD of the power system random variables making rare loss of load events more likely to be drawn. When the number of states needed to be evaluated is decreased and at the same time preserving the estimator accuracy, the efficiency of the approach will wholly computationally enhance.
The application of the proposed approach in reliability evaluation could enable to enlarge the sample space with the probabilistic modeling of more uncertainties and so matching the reality of the proposed EPS model. The impact of transmission network outages, and spatially correlated demand and renewable energy resources model, could be incorporated into the EPS model. This is accomplished by considering electricity demand and weather variables uncertainties based on real historical data. Use of real data and proper represent the uncertainties give a more realist attitude of power grid performance on the basis of actual reliability indicators and so proper reserve allocation which are dispatched according to the customers’ reliability requirements and the location of renewable energy resources.
This realistic model integrated with the efficient ECE-IS method can also be included into the many problems in both operation and planning phases, such as the proper allocation of spinning reserve to allow more integration of renewable powers and improve system and nodal reliability. Using adequacy indices assessments and knowing the critical nodes during system disturbance, planners can better manage the penetration and coordination of renewable energy resources, ensuring sustainable and

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reliable operation at both the system and nodal level. In the context of power system operation, operators schedule the generating units and allocate enough generation reserve amounts to ensure a lower the probability of load loss than the maximum allowed.
Research methodology. The research is carried out on the basis of the theoretical foundations of electrical engineering, probability theory and mathematical statistics. The considered methods and algorithms are tested on EPS systems. Evaluation of the effectiveness in terms of the computational efficiency and accuracy is estimated by the MCS method. Moreover, the practical applicability of the developed algorithms with respect to the reliability assessment problem is highlighted. For calculations and software implementation of the algorithms, the MATLAB software package is used. All calculations are executed on an Intel Core i5-8 G memory computer using MATLAB 2017.
The main contributions of the dissertation submitted for defense:
• The assessment of the efficiency and accuracy of the probabilistic-analytical methods and procedures with respect to the reliability evaluation problem.
• The analysis and identification of the best importance sampling strategy in estimating the optimal IS distribution of the uncertain input variables for the composite system reliability assessment problem.
• Enhancing the existing cross entropy-based importance sampling procedure to extract most the rare loss of load events in power systems;
• Integrating the ECE-IS procedure in the reliability evaluation framework that can greatly accelerate the calculation efficiency of the MCS method while not losing the accuracy. The computational efficiency and adaptability of the proposed approach are validated by the results of case studies.
• The analysis and identification of the accurate probabilistic model to handle with the historical real data complexity of the demand and weather variables for proper incorporating the random variation and chronological characteristics of electricity

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demand and renewable energy resources (wind- solar) in the reliability assessment
problem.
• Evaluating accurately and efficiently power system annual reliability indices with
integration of a large-scale PV power stations and wind farms using the ECE-IS technique. The ECE-IS will assist IS in sampling the region of interest for the system reliability indicators (i.e., the region in which the wind farms and PV power stations have lower power generation). Moreover, it preserves the dependence structure of and renewable and load powers in the reliability evaluation procedure, thus the efficiency degradation is avoided. This ensures that the reliability indices are evaluated with an acceptable computation burden.
The author’s personal contribution is the development of software for testing the effectiveness of existing and proposed statistical algorithms and methods; the proposition of new efficient simulation techniques for solving the problem of reliability assessment; studying the problem of selection of probabilistic approach which is capable of accurately modelling the uncertainties within the power system network in spite of their probability distribution and characterize the correlation among uncertainties in the power network.
The reliability of the results is validated by the results of computational tests on 5-node and IEEE-RTS 79 test schemes.
Approbation of work results were reported and discussed at 4 conferences:
• International Scientific Conference Energy Management of Municipal Facilities and Sustainable Energy Technologies (EMMFT 2018) Samara, Russia;
• Scientific Symposium on Electric Power Engineering (ELEKTROENERGETIKA 2019), Stara Lesna, Slovakia;
• 2019 IEEE 60th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON), 2019, Riga, Latvia.

• International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM 2020), Sochi, Russia.
Publications: According to the results of the work, 7 works were published and indexed in the international citation bases Scopus and Web of Science.
Dissertation structure. The dissertation consists of an introduction, 4 chapters, a conclusion, symbol list and 140 reference list. It contains 110 pages, 19 figures and 10 tables.