ИНСТИТУТ ЗА ПЕЕС

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проф. д-р Мирко Тодоровски - список на трудови

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Todorovski M, Angelov Jordančo and Vuletić J (2021), "Solving Tridiagonal Symmetric Systems of Equations Using Circuit Theory Approach", IAENG International Journal of Computer Science., Sep, 2021. Vol. 48(3), pp. 663-671.

[Abstract] [BibTeX] [URL]
Abstract: This paper introduces a novel solution method for solving symmetric tridiagonal systems. The main idea behind it is to construct a specific electric circuit with the same node-voltage equations as the original system. This circuit has a specific "ladder" structure that is efficiently solved using a methodology known as admittance summation method. The proposed method avoids possible zero divisions by exploiting a specific circuit structure. This specific property is an equivalent to a pivoting strategy used in other methods. Performance tests show that the proposed method is comparable to Thomas algorithm, Gaussian elimination adapted for tridiagonal systems and Matlab backslash operator. The procedure executes O(N) times meaning that computation time is linearly proportional to system size. The whole method is coded very concisely.
BibTeX: 
@article{Todorovski2021,
  author = {Todorovski, Mirko and Angelov, Jordančo, and Vuletić, Jovica},
  title = {Solving Tridiagonal Symmetric Systems of Equations Using Circuit Theory Approach},
  journal = {IAENG International Journal of Computer Science},
  year = {2021},
  volume = {48},
  number = {3},
  pages = {663-671},
  url = {http://www.iaeng.org/IJCS/issues_v48/issue_3/IJCS_48_3_24.pdf}
}
Grcev L, Markovski B and Todorovski M (2021), "General Formulas for Lightning Impulse Impedance of Horizontal and Vertical Grounding Electrodes", IEEE Transactions on Power Delivery., Aug, 2021. Vol. 36(4), pp. 2245-2248.

[Abstract] [BibTeX] [DOI]
Abstract: Voltage drop developed between the grounding electrode under lightning current and distant neutral ground determines the protection efficiency. The peak value of such voltage can be computed from known impulse impedance and current peak value. For the first time, in this letter, general formulas are derived for impulse impedance of horizontal and vertical electrodes valid for any length up to 100 m, soil's resistivity of 30 to 1000 Ωm, and current impulse front time of 0.2 to 10 μs. Waveforms of typical lightning impulses given in IEC standards are used, but it is shown that results are also relevant for other impulse waveforms. Soil ionization effects are taken into account, and the accuracy of the formulas is investigated. New formulas enable an estimate of lightning protection grounding's surge efficiency in a wide range of practical situations.
BibTeX: 
@article{Grcev2021,
  author = {Grcev, Leonid and Markovski, Blagoja and Todorovski, Mirko},
  title = {General Formulas for Lightning Impulse Impedance of Horizontal and Vertical Grounding Electrodes},
  journal = {IEEE Transactions on Power Delivery},
  year = {2021},
  volume = {36},
  number = {4},
  pages = {2245-2248},
  doi = {10.1109/TPWRD.2021.3080137}
}
Rajicic D and Todorovski M (2021), "Participation of Every Generator to Loads, Currents and Power Losses", IEEE Transactions on Power Systems., March, 2021, Vol. 36(2), pp. 1638-1640.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: Among other things, in a detailed analysis of circumstances in power systems of great importance is the knowledge on contribution of individual generators to loads, and to currents and power losses in network elements. This work proposes an efficient method for obtaining these details. The method uses results of a power flow calculation, utilizes specific power system model, and applies the superposition theorem. The method does not contain problematic assumptions or simplifications and it is easy to apply. It allows getting important facts enabling us to establish transparent and non-discriminatory relationships between net-work operators, electricity producers and consumers.
BibTeX: 
@article{Rajicic2020,
  author = {D. Rajicic and M. Todorovski},
  title = {Participation of Every Generator to Loads, Currents and Power Losses},
  journal = {IEEE Transactions on Power Systems},
  year = {2021},
  volume = {36},
  number = {2},
  pages = {1638-1640},
  url = {https://ieeexplore.ieee.org/document/9293183},
  doi = {10.1109/TPWRS.2020.3044485}
}
Todorovski M and Rajičić D (2020), "Contribution of generator-load pairs in distribution networks power losses", International Journal of Electrical Power & Energy Systems. Vol. 115, pp. 105433.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: The focus of the research presented here is developing a method to calculate contribution of each generator-load pair in total distribution network power losses. To do this we calculate current component from any generator to any load and then multiply each of these conjugate current components by difference between corresponding generator node voltage and load node voltage. This way there are no quadratic expressions and problems with non-separability of losses. Also, the procedure breaks down the losses in such a way that one may investigate how each power transaction contributes to the losses. The idea to create such kind of method is to assist network users (producers and consumers) obtaining detailed information about distribution of power losses among network branches, and base on this information to consider corresponding transparent and non-discriminatory actions. Developing the method, no problematic assumptions or simplifications were used. Hence, the method is exact and do not consider privilege to any network user. In addition, it handles PV nodes without additional inconveniencies. Accordingly comparing this method with methods allocating losses to nodes it is understandable to identify dissimilarities. Moreover, this version of the method is applicable to radial distribution network with neglected influence of line shunt susceptances. The whole procedure is illustrated with a simple numerical example and it is also applied to a bigger system. The MATLAB code is given as an open-source for further research.
BibTeX: 
@article{Todorovski2020,
  author = {Mirko Todorovski and Dragoslav Rajičić},
  title = {Contribution of generator-load pairs in distribution networks power losses},
  journal = {International Journal of Electrical Power & Energy Systems},
  year = {2020},
  volume = {115},
  pages = {105433},
  url = {http://www.sciencedirect.com/science/article/pii/S0142061519304661},
  doi = {10.1016/j.ijepes.2019.105433}
}
Taseska-Gjorgievska V, Todorovski M, Markovska N and Dedinec A (2019), "An Integrated Approach for Analysis of Higher Penetration of Variable Renewable Energy: Coupling of the Long-Term Energy Planning Tools and Power Transmission Network Models", Journal of Sustainable Development of Energy, Water and Environment Systems.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: Many studies and scientific papers have been published that consider the integration of renewable sources in energy systems, using the least-cost optimization models as a long-term generation expansion planning tool. Supplementary to these analyses, this paper focuses on the transmission network capacity for acceptance of variable renewable energy. The hypothesis is that the simplified electric power transmissions system in the long-term planning modelling tools does not reflect properly the capacity for integration of the variable renewable energy. An integrated approach is applied with aim to incorporate the grid expansion needs and costs (using Direct Current Load Flow analysis), necessary for increased renewable electricity penetration. The already developed MARKAL – Macedonia model will be used as a case study. After several iterations and feedback loops between the MARKAL- Macedonia and the network model, the expected outcome is to achieve a new cost-effective solution for deployment of variable energy on a larger scale.
BibTeX: 
@article{Gjorgievska2018journal,
  author = {Verica Taseska-Gjorgievska and Miko Todorovski and Natasa Markovska and Aleksandar Dedinec},
  title = {An Integrated Approach for Analysis of Higher Penetration of Variable Renewable Energy: Coupling of the Long-Term Energy Planning Tools and Power Transmission Network Models},
  journal = {Journal of Sustainable Development of Energy, Water and Environment Systems},
  year = {2019},
  url = {http://dx.doi.org/10.13044/j.sdewes.d7.0264},
  doi = {10.13044/j.sdewes.d7.0264}
}
Rajicic D and Todorovski M (2018), "A Double-Exponential Lightning Current Function Suitable for Use of Different Sets of Input Data", IEEE Transactions on Power Delivery., Aug, 2018. Vol. 33(4), pp. 2053-2055.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: A function to simulate lightning return stroke current as a sum of two exponential terms is presented. The exponent of the first term is a linear function of time, while the exponent of the second term is a power function of time with degree n. Compared with the function from IEC 62305-1, the proposed function offers slightly different front of the current impulse. In addition, this letter gives details how to obtain parameters of the proposed function that satisfy the given requirements.
BibTeX: 
@article{RajicicTodorovski2018,
  author = {D. Rajicic and M. Todorovski},
  title = {A Double-Exponential Lightning Current Function Suitable for Use of Different Sets of Input Data},
  journal = {IEEE Transactions on Power Delivery},
  year = {2018},
  volume = {33},
  number = {4},
  pages = {2053-2055},
  url = {https://doi.org/10.1109/TPWRD.2017.2711268},
  doi = {10.1109/TPWRD.2017.2711268}
}
Angelov J, Taleski R, Vuletic J, Todorovski M, Krstevski P and Krkoleva-Mateska A (2017), "Application of Reduced PTDF Matrix in Iterative Modified DC Network Model for Cross–border Capacity Calculation with Consideration of Reactive Power Flow Constraints", In IEEE EUROCON 2017., July, 2017. (214)

[Abstract] [BibTeX] [DOI] [URL]
Abstract: One of the biggest threats for the security of power grids are congestion of cross-border lines and congestion in the network itself as result of parallel flows. Nowadays, occurrence of congestion is a result of limited network transfer capacities as a direct consequence of increased power transactions. One of the reasons for cross-border congestions are the unreal cross-border capacities calculations. This is a result of assumptions and simplifications made in the methodologies for total transfer capacity calculation. In this paper, we propose an iterative optimization algorithm based on modified DC network model that takes into consideration reactive power flows and all the constraints that comes forward. The proposed methodology is based on reduced Power Transfer Distribution Factor (PTDF) Power Transfer Distribution Factor) matrix. This approach successfully solves two DC Optimal Power Flow (OPF) problems: cost minimization and total transfer capacity calculation. For testing purposes IEEE test network RTS 96 is used.
BibTeX: 
@inproceedings{Angelov2017,
  author = {Jordancho Angelov and Rubin Taleski and Jovica Vuletic and Mirko Todorovski and Petar Krstevski and Aleksandra Krkoleva-Mateska},
  title = {Application of Reduced PTDF Matrix in Iterative Modified DC Network Model for Cross–border Capacity Calculation with Consideration of Reactive Power Flow Constraints},
  booktitle = {IEEE EUROCON 2017},
  year = {2017},
  number = {214},
  url = {https://doi.org/10.1109/EUROCON.2017.8011148},
  doi = {10.1109/EUROCON.2017.8011148}
}
Gjorgievski V and Todorovski M (2017), "Optimization of Complex Energy Systems", Journal of Electrical Engineering and Information Technologies - JEEIT. Vol. 2(2), pp. 113-120.

[Abstract] [BibTeX] [URL]

Abstract: According to the common practice different energy systems are analyzed separately, without taking into consideration their mutual dependence. The goal of this paper is to illustrate the modeling and optimization of complex systems, i.e. multiple-energy carrier systems, by using the energy hub methodology. A multiple-energy carrier system consists of different energy infrastructures and serves various types of energy demands, such as electricity, heat etc. The energy hub concept is thus implemented in the formulation of the economic dispatch problem for a complex energy system. Moreover, the paper contains a linear optimal power flow formulation of a complex system with multiple energy hubs interconnected with the power grid. The analysis will be conducted over simply structured systems with the aim of illustrating the idea of integrated modeling and the comparison of the system’s operating points obtained by separate and integrated optimization.
BibTeX: 
@article{Gjorgievski2017,
  author = {Vladimir Gjorgievski and Mirko Todorovski},
  title = {Optimization of Complex Energy Systems},
  journal = {Journal of Electrical Engineering and Information Technologies - JEEIT},
  year = {2017},
  volume = {2},
  number = {2},
  pages = {113-120},
  url = {http://jeeit.feit.ukim.edu.mk/index.php/jeeit/article/view/74}
}
Pavlovski M, Gajduk A, Todorovski M and Kocarev L (2017), "Improving Power Grid Stability With Communication Infrastructure", IEEE Journal on Emerging and Selected Topics in Circuits and Systems., Sept, 2017. Vol. 7(3), pp. 349-358.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: Efficient control of power systems is becoming increasingly difficult as they gain in complexity and size. By considering a power grid and a communication infrastructure as a multiplex network, we propose an automatic control strategy that regulates the mechanical power output of the generators based on information obtained via communication links (wireless or wired). An algorithm that optimizes steady-state stability of a power grid by iteratively adding communication links is presented. The proposed control scheme is successfully applied to the IEEE New England and the IEEE RTS 96 power systems, leading to a significant increase in the steady-state stability of the systems and an improvement in their overall robustness. The resulting communication network topology differs significantly from the transmission grid topology. This shows how complex the steady-state control for power systems is, influenced by the generators' configuration, the transmission network topology, and the manner by which control is executed.
BibTeX: 
@article{PavlovskiGajdukEtAl2017,
  author = {M. Pavlovski and A. Gajduk and M. Todorovski and L. Kocarev},
  title = {Improving Power Grid Stability With Communication Infrastructure},
  journal = {IEEE Journal on Emerging and Selected Topics in Circuits and Systems},
  year = {2017},
  volume = {7},
  number = {3},
  pages = {349-358},
  url = {https://doi.org/10.1109/JETCAS.2017.2672679},
  doi = {10.1109/JETCAS.2017.2672679}
}
Zdraveski V, Todorovski M, Trajanov D and Kocarev L (2017), "Dynamic Load Balancing and Reactive Power Compensation Switch embedded in Power Meters", IEEE Transactions on Circuits and Systems II: Express Briefs., April, 2017. Vol. 64(4), pp. 422-426.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: This paper proposes a dynamic intelligent load balancing and reactive power compensation switch plugin for power meters and a smart scalable system architecture applicable as addon on top of the existing power distribution networks. The load balancing module will improve the load balance in a network and thus decrease the power losses, whereas the distributed reactive power compensator will decrease the total reactive power. The novel approach is presented from its IT/networks perspective as well as from the physical layer with oscilloscope measurements and time analysis of the phase swapping event.
BibTeX: 
@article{ZdraveskiTodorovskiEtAl2017,
  author = {V. Zdraveski and M. Todorovski and D. Trajanov and L. Kocarev},
  title = {Dynamic Load Balancing and Reactive Power Compensation Switch embedded in Power Meters},
  journal = {IEEE Transactions on Circuits and Systems II: Express Briefs},
  year = {2017},
  volume = {64},
  number = {4},
  pages = {422-426},
  url = {http://dx.doi.org/10.1109/TCSII.2016.2570338},
  doi = {10.1109/TCSII.2016.2570338}
}
Vuletić J and Todorovski M (2016), "Optimal Capacitor Placement in Distorted Distribution Networks with Different Load Models Using Penalty Free Genetic Algorithm", International Journal of Electrical Power & Energy Systems., June, 2016. Vol. 78, pp. 174-182.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: Abstract Genetic Algorithm with special constraint handling procedure is proposed for the discrete optimization problem of capacitor placement and sizing in distribution system for cost reduction and power quality improvement. We use gene encoding that enables simple integer representation of possible different number of capacitors of various standard sizes to be placed on a bus. A pair-wise comparison in tournament selection operator is used so that it does not require any penalty parameter tuning, thus avoiding the most difficult aspect of the selection of appropriate penalty parameters. Proposed Penalty Free Genetic Algorithm (PFGA) is tested on 18-bus, 69-bus and 141-bus systems and the obtained results are better than the results from other methods. Simulations with different load models are also performed. It is shown that load models where active and reactive loads are voltage dependent, such as residential, commercial and industrial, constant Z and constant I model lead to completely different solutions. Therefore, careful load modeling should be put in place in order to obtain more realistic picture of the total savings.
BibTeX: 
@article{VuleticTodorovski2016,
  author = {J. Vuletić and M. Todorovski},
  title = {Optimal Capacitor Placement in Distorted Distribution Networks with Different Load Models Using Penalty Free Genetic Algorithm},
  journal = {International Journal of Electrical Power & Energy Systems},
  year = {2016},
  volume = {78},
  pages = {174-182},
  url = {http://dx.doi.org/10.1016/j.ijepes.2015.11.065},
  doi = {10.1016/j.ijepes.2015.11.065}
}
Angelov J, Vuletić J, Ačkovski R and Todorovski M (2015), "An Extension in Cable Modeling for Grounding System", IEEE Transactions on Industry Applications., Nov.-Dec., 2015. Vol. 51(6), pp. 5086-5094.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: The building blocks of the equivalent circuit of a complex grounding system are individual equivalent circuits of all system elements, which are represented with their equivalent π circuits. In this paper, we focus on underground single-core cable lines with a ground return wire, which are very common elements in distribution networks. We model the cable line as a four-phase distributed parameter line and take into account all self-impedance and mutual impedance of three cable sheaths and the ground return wire. In the model, we allow for variable earth resistivity along the cable path and cases with the ground return wire placed in full cable length or in a portion of it. The developed π-equivalent circuit is nonsymmetric, which is a step forward in cable modeling for grounding systems analysis. We have analyzed a simple distribution system where we have shown that, with the use of π-equivalent circuits, we can easily calculate voltages in grounding systems. The proposed methodology offers a possibility to calculate voltage and current distribution along the cable line in all four conductors. The results show that costs savings are possible if the ground return wire is not laid in full cable length. The length of the ground return wire is determined so that the voltage magnitude safety levels are not violated.
BibTeX: 
@article{AngelovVuleticEtAl2015,
  author = {J. Angelov and J. Vuletić and R. Ačkovski and M. Todorovski},
  title = {An Extension in Cable Modeling for Grounding System},
  journal = {IEEE Transactions on Industry Applications},
  year = {2015},
  volume = {51},
  number = {6},
  pages = {5086-5094},
  url = {http://dx.doi.org/10.1109/TIA.2015.2409807},
  doi = {TIA.2015.2409807}
}
Rajičić D and Todorovski M (2015), "Two-Component Current Waveform for Lightning Simulation", IEEE Transactions on Electromagnetic Compatibility., October, 2015. Vol. 57(5), pp. 1062-1069.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: A new model to simulate return stroke lightning current is presented. The idea for the model arose from the observation that measured lightning current has two quite different parts (fast rise and slow decay). Experimental measurement differentiates three segments in the rising portion: 1) increasing rate of rise, 2) relatively constant rate of rise, and 3) decreasing rate of rise. We propose two functions to represent the return stroke current waveshape, which closely resemble the first and the third segments, and compare them with previously developed models. In fact, we develop two versions of the proposed model: 1) version A: which creates waveshapes close to the waveshapes obtained by the model given in International Standard IEC 62305-1, and 2) version B: which creates waveshapes more similar to the mean waveshapes obtained by the measurement. It is worth pointing out that in both versions we can calculate model parameters using simple formulas.
BibTeX: 
@article{RajicicTodorovski2015,
  author = {D. Rajičić and M. Todorovski},
  title = {Two-Component Current Waveform for Lightning Simulation},
  journal = {IEEE Transactions on Electromagnetic Compatibility},
  year = {2015},
  volume = {57},
  number = {5},
  pages = {1062-1069},
  url = {http://dx.doi.org/10.1109/TEMC.2015.2420581},
  doi = {10.1109/TEMC.2015.2420581}
}
Zdraveski V, Todorovski M and Kocarev L (2015), "Dynamic Intelligent Load Balancing in Power Distribution Networks", International Journal of Electrical Power & Energy Systems., December, 2015. Vol. 73, pp. 157-261.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: Using hierarchical, client–server addressing concepts and identifying the load balancing problem among phases in 3-phase systems, we propose a novel, very simple algorithm for dynamic intelligent load balancing (DILB), that decreases the power losses in a power distribution network (PDN). Our solution is easily applicable to every part of a PDN, without essential changes to the last-line power installation. We present the DILB-extended PDN architecture, the algorithm itself as well as the results of the simulation on the well known IEEE 34-Bus, 37-Bus and 123-Bus networks that confirm the expected level of active power losses minimization.
BibTeX: 
@article{ZdraveskiTodorovskiEtAl2015,
  author = {V. Zdraveski and M. Todorovski and L. Kocarev},
  title = {Dynamic Intelligent Load Balancing in Power Distribution Networks},
  journal = {International Journal of Electrical Power & Energy Systems},
  year = {2015},
  volume = {73},
  pages = {157-261},
  url = {http://dx.doi.org/10.1016/j.ijepes.2015.05.012},
  doi = {10.1016/j.ijepes.2015.05.012}
}
Gajduk A, Todorovski M and Kocarev L (2014), "Stability of power grids: an overview", European Physical Journal - Special Topics., June, 2014. Vol. 223, pp. 2387-2409.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: Transient stability and steady-state (small signal) stability in power girds are reviewed. Transient stability concepts are illustrated with simple examples; in particular, we consider three methods for computing region of attraction: time-simulations, extended Lyapunov function, and sum of squares optimization method. We discuss steady state stability in power systems, and present an example of a feedback control via a communication network for the 10 Unit 39 Bus New England Test system.
BibTeX: 
@article{GajdukTodorovskiEtAl2014,
  author = {A. Gajduk and M. Todorovski and Ljupco Kocarev},
  title = {Stability of power grids: an overview},
  journal = {European Physical Journal - Special Topics},
  year = {2014},
  volume = {223},
  pages = {2387-2409},
  url = {http://dx.doi.org/10.1140/epjst/e2014-02212-1},
  doi = {10.1140/epjst/e2014-02212-1}
}
Gajduk A, Todorovski M, Kurths J and Kocarev L (2014), "Improving power grid transient stability by plug-in electric vehicles", New Journal of Physics., November, 2014. Vol. 16

[Abstract] [BibTeX] [DOI] [URL]
Abstract: Plug-in electric vehicles (PEVs) can serve in discharge mode as distributed energy and power resources operating as vehicle-to-grid (V2G) devices and in charge mode as loads or grid-to-vehicle devices. It has been documented that PEVs serving as V2G systems can offer possible backup for renewable power sources, can provide reactive power support, active power regulation, load balancing, peak load shaving, can reduce utility operating costs and can generate revenue. Here we show that PEVs can even improve power grid transient stability, that is, stability when the power grid is subjected to large disturbances, including bus faults, generator and branch tripping, and sudden large load changes. A control strategy that regulates the power output of a fleet of PEVs based on the speed of generator turbines is proposed and tested on the New England 10-unit 39-bus power system. By regulating the power output of the PEVs we show that (1) speed and voltage fluctuations resulting from large disturbances can be significantly reduced up to five times, and (2) the critical clearing time can be extended by 20–40%. Overall, the PEVs control strategy makes the power grid more robust.
BibTeX: 
@article{GajdukTodorovskiEtAl2014a,
  author = {A. Gajduk and M. Todorovski and J. Kurths and L. Kocarev},
  title = {Improving power grid transient stability by plug-in electric vehicles},
  journal = {New Journal of Physics},
  year = {2014},
  volume = {16},
  url = {http://dx.doi.org/10.1088/1367-2630/16/11/115011},
  doi = {10.1088/1367-2630/16/11/115011}
}
Todorovski M (2014), "Transformer Voltage Regulation – Compact Expression Dependent on Tap Position and Primary/Secondary Voltage", IEEE Transactions on Power Delivery., June, 2014. Vol. 29(3), pp. 1516-1517.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: This letter presents a compact transformer voltage regulation expression which accounts for off-nominal tap position and voltage deviation from the nominal value. The expression is validated through comparison with the common expressions used in the literature. It is shown that the primary/secondary voltage variation has a certain influence on the results which were not taken into account in previous compact forms of the voltage regulation expression.
BibTeX: 
@article{Todorovski2014,
  author = {M. Todorovski},
  title = {Transformer Voltage Regulation – Compact Expression Dependent on Tap Position and Primary/Secondary Voltage},
  journal = {IEEE Transactions on Power Delivery},
  year = {2014},
  volume = {29},
  number = {3},
  pages = {1516-1517},
  url = {http://dx.doi.org/10.1109/TPWRD.2014.2311959},
  doi = {10.1109/TPWRD.2014.2311959}
}
Todorovski M and Ačkovski R (2014), "Reduction of PTDF Matrix and Its Application in DC Optimal Power Flow", International Transactions on Electrical Energy Systems., April, 2014.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: The paper presents an approach where traditional Power Transfer Distribution Factors (PTDF) matrix is reduced in size so that it reflects sensitivities of branch flows to changes in nodal power injections at generator buses only. The advantage of the reduced PTDF matrix is in both reductions of decision variables in the optimization procedure and number of columns in branch flow constraints matrix. Furthermore, the number of rows is also reduced on the basis of a simple check, which effectively detects non-binding branch flow limits allowing corresponding rows of the matrix to be omitted. The reduced PTDF matrix was successfully applied in solving two direct current optimal power flow problems: cost minimization and total transfer capacity calculation.
BibTeX: 
@article{TodorovskiAckovski2014,
  author = {M. Todorovski and R. Ačkovski},
  title = {Reduction of PTDF Matrix and Its Application in DC Optimal Power Flow},
  journal = {International Transactions on Electrical Energy Systems},
  year = {2014},
  url = {http://dx.doi.org/10.1002/etep.1936},
  doi = {10.1002/etep.1936}
}
Todorovski M and Ačkovski R (2014), "Equivalent Circuit of Single-Core Cable Lines Suitable for Grounding Systems Analysis under Line to Ground Faults", IEEE Transactions on Power Delivery., April, 2014. Vol. 29(2), pp. 751-759.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: This paper presents two approaches where the single-core cable line and an additional conductor laid in parallel can be reduced to a simple equivalent π-circuit containing an active element beside the usual passive impedances. The parameters of the equivalent circuit are calculated using a numerical approach where the distributed parameter line was discretized and an analytical approach is based on the wave propagation theory. A series of tests has been performed to determine error levels in both cases showing that they are less than 1%. With numerical examples, we show that the cable equivalent circuit offers a simple way to calculate voltages in complex grounding systems. The results are in good agreement with the previously published calculated and/or measured values. Both approaches offer the possibility of calculating voltage and current distribution along the cable line which gives insight into the significance of each cable component in the complex grounding system.
BibTeX: 
@article{TodorovskiAckovski2014a,
  author = {M. Todorovski and R. Ačkovski},
  title = {Equivalent Circuit of Single-Core Cable Lines Suitable for Grounding Systems Analysis under Line to Ground Faults},
  journal = {IEEE Transactions on Power Delivery},
  year = {2014},
  volume = {29},
  number = {2},
  pages = {751-759},
  url = {http://dx.doi.org/10.1109/TPWRD.2013.2277887},
  doi = {10.1109/TPWRD.2013.2277887}
}
Vuletić J and Todorovski M (2014), "Optimal Capacitor Placement in Radial Distribution Systems Using Clustering Based Optimization", International Journal of Electrical Power & Energy Systems., November, 2014. Vol. 62, pp. 229-236.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: A Clustering Based Optimization (CBO) for the discrete optimisation problem of fixed shunt capacitor placement and sizing is presented. We minimize the sum of costs for power/energy losses and capacitor costs. Over-compensation and voltage constraints are also taken into consideration. CBO is based on a simple search which iteratively loops through network buses and places capacitors at locations that yield maximum reduction of losses in the objective function. The effectiveness of the proposed approach is demonstrated on a 22-bus, 34-bus, 69-bus and 85-bus distribution systems. The CBO results are better than the results from other methods from recent papers which include: Fuzzy Genetic Algorithm (FGA), Direct Search Algorithm (DSA), Teaching Learning Based Optimization (TLBO), Cuckoo Search (CS), Self Adaptive Harmony Search Algorithm (SAHSA) and Artificial Bee Colony (ABC). In addition, for all cases, the proposed method gives repetitive and unique results in significantly shorter computation time.
BibTeX: 
@article{VuleticTodorovski2014,
  author = {J. Vuletić and M. Todorovski},
  title = {Optimal Capacitor Placement in Radial Distribution Systems Using Clustering Based Optimization},
  journal = {International Journal of Electrical Power & Energy Systems},
  year = {2014},
  volume = {62},
  pages = {229-236},
  url = {http://dx.doi.org/10.1016/j.ijepes.2014.05.001},
  doi = {j.ijepes.2014.05.001}
}
Todorovski M and Rajičić D (2006), "An Initialization Procedure in Solving Optimal Power Flow by Genetic Algorithm", IEEE Transaction on Power Systems. Vol. 21(2), pp. 480-487.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: The recently published idea of treating voltage angles at generator-buses as control variables enables to obtain voltages at load-buses with less computation. However, application of this approach in solving the optimal power flow problem by genetic algorithms may be ineffective if starting values of voltage angles are selected quite randomly. To overcome these difficulties, a new procedure for selection of an initial set of complex voltages at generator-buses is proposed in this paper. With this procedure, one can start the optimization process (i.e., genetic algorithm) with a set of control variables, causing few or no violations of constraints. The application of voltage angles at generator-buses as control variables and the proposed initialization procedure is illustrated on the IEEE test systems. The obtained results are analyzed and compared with the results from the literature. They are competitive, with computational time drastically reduced.
BibTeX: 
@article{TodorovskiRajicic2006,
  author = {M. Todorovski and D. Rajičić},
  title = {An Initialization Procedure in Solving Optimal Power Flow by Genetic Algorithm},
  journal = {IEEE Transaction on Power Systems},
  year = {2006},
  volume = {21},
  number = {2},
  pages = {480-487},
  url = {http://dx.doi.org/10.1109/TPWRS.2006.873120},
  doi = {10.1109/TPWRS.2006.873120}
}
Todorovski M and Rajičić D (2003), "Handling Three-Winding Transformers and Loads in Short Circuit Analysis by the Admittance Summation Method", IEEE Transaction on Power Systems., August, 2003. Vol. 18(3), pp. 993-1000.

[Abstract] [BibTeX] [DOI] [URL]
Abstract: The admittance summation method is efficient in short circuit analysis of radial and weakly meshed networks. It is especially powerful if all node loads can be represented as any combination of constant impedance and constant current load component. However, in the existing literature one cannot find any explanation how to handle power transformer in that approach. For that reason, the corresponding equations have been developed in this paper along with a procedure for development of a three-winding transformer admittance matrix. In addition, a procedure for handling an arbitrary load was proposed. A large number of tests were performed and results were compared with that obtained by the previously published method. As an illustration, some of the results for single fault currents are presented. It can be concluded that the proposed approach makes the admittance summation method capable to take into account all network elements in a proper way.
BibTeX: 
@article{TodorovskiRajicic2003,
  author = {M. Todorovski and D. Rajičić},
  title = {Handling Three-Winding Transformers and Loads in Short Circuit Analysis by the Admittance Summation Method},
  journal = {IEEE Transaction on Power Systems},
  year = {2003},
  volume = {18},
  number = {3},
  pages = {993-1000},
  url = {http://dx.doi.org/10.1109/TPWRS.2003.814850},
  doi = {10.1109/TPWRS.2003.814850}
}