This article presents a method for stability analysis of hybrid power systems with a high share of renewable energy sources, particularly photovoltaic generators, based on the dq0-transformation (Park’s transformation). The key feature of this approach is the unification of all system components – synchronous generators, network elements, and power inverters – into a single generalized reference frame rotating at synchronous speed. This enables the construction of a holistic dynamic model of complex power systems that maintains high accuracy across a wide frequency range while preserving time-invariance for steady-state analysis.
The relevance of this research stems from the critical need for advanced mathematical modeling methods in electric power systems undergoing structural transformations due to integration of renewable-based distributed generation. The extensive integration of stochastic generation sources fundamentally alters power system dynamics, creating challenges for traditional modeling approaches. Existing methods demonstrate limited effectiveness in analyzing transients under high penetration of intermittent generation. Consequently, developing a mathematical framework for modeling hybrid power system dynamics represents a significant scientific challenge essential for ensuring reliable operation and sustainable development of power systems. Traditional phase-coordinate models provide accuracy but are non-stationary, complicating stability analysis, while quasi-static models, though stationary, neglect high-frequency dynamics. The proposed method addresses this methodological gap through a unified approach to modeling heterogeneous power system components.
The work details the mathematical apparatus for transforming equations of main system components into a unified coordinate system. For passive network elements (inductances, capacitances, resistors), state equation transformation accounts for the transformation operator derivative. The synchronous generator is represented by a physical salient-pole machine model considering mutual influence of magnetic fields along d- and q-axes, winding active resistances, and rotor circuit dynamics. Described by six state variables, this model incorporates inductive parameters ignored in simplified models. The photovoltaic generator utilizes an inverter model with DC-link voltage control loop employing PI-controller and output capacitive storage. The procedure for integrating inverter output variables into the common coordinate system is demonstrated.
A crucial methodological aspect is the network model reduction procedure. We describe a node elimination algorithm for buses unconnected to generators or loads, reducing problem dimensionality and focusing analysis on key generator bus dynamics. Reduction is achieved by controlling corresponding bus input variables to zero their outputs, followed by state vector transformation and new dynamic model formation using matrix algebra methods like LU-decomposition. This procedure is particularly important for large power systems where full models may contain redundant research information.
The method was tested through numerical experiments using MATPOWER test networks, including a modified IEEE 14-bus system with partial conventional generator replacement by photovoltaic stations. Comparative analysis of quasi-static, phase-domain (abc), and dq0-models was performed, along with small-signal dynamics investigation through linearization and eigenvalue analysis. Particular attention was given to verifying model adequacy under various system parameter variation scenarios.
Initial four-bus network simulation confirmed identical steady-states across all three model types. Phase-domain and dq0-models showed complete transient response agreement, while the quasi-static model inadequately represented high-frequency electromagnetic transients. Computational efficiency assessment analyzed matrix sparsity and non-zero element counts, revealing comparable abc and dq0 model parameters, demonstrating dq0-approach practicality for complex system modeling without significant computational burden increase.
A hybrid system based on modified IEEE 14-bus network was investigated, with synchronous generators at buses 6 and 8 replaced by photovoltaic stations. A complete nonlinear dq0-coordinate system model was developed, incorporating two synchronous generators, two photovoltaic inverters, passive network, and infinite bus. Steady-state parameters were obtained from power flow solutions. This test case enables investigation of mutual influence between conventional and renewable generation under varying parameters.
Stability analysis employed individual component model linearization around operating points followed by general state-space model formation. Frequency response analysis (Bode plots) of state-space equations examined inter-machine connections from mechanical to electrical power, revealing significant mutual influence near 30 rad/s resonance frequency. Root locus analysis tracked dominant eigenvalue trajectories under external disturbances: stepped mechanical power increase and photovoltaic power reduction. Pole migration toward imaginary axis indicated reduced stability margin and response speed under loading. Photovoltaic inverter power variation proved less dynamically significant than synchronous generator power changes, attributable to lower rated power in this test case.
The results demonstrate how synchronous generator and photovoltaic inverter power variations affect system stability and dynamics, confirming the approach’s effectiveness for large-scale hybrid power system modeling. The developed methodology provides a formalized tool for determining maximum permissible renewable generation shares while maintaining static and dynamic stability constraints. These findings enable future research into coordinated control of heterogeneous generators in complex power systems.

This study proposes a new technology for increasing the efficiency of solar water heating systems using a heating vapor dynamic circuit. The variant of assimilation of solar energy and transfer of the obtained heat into the volume of heated water is considered based on the application of the paradynamic effect, the essence of which is the use of a heating circuit, partially (20-30% of the circuit volume) filled with a low-boiling liquid (ELF), the vapors of which enter the heat exchanger-condenser located in the tank-pool with heated water. The results of the analysis of the efficiency of a number of CALs are presented, which made it possible to select the optimal low-boiling coolants. The efficiency of water heating systems with a vapor-dynamic circuit was experimentally investigated, which showed a significant increase in water temperature in the daytime cycle when gasoline and acetone were used as an intermediate circuit. It is shown that the proposed technological scheme of water heating using a vapor-dynamic circuit with a low-boiling coolant allows for effective heat transfer without the use of pumping equipment using solar collectors of the simplest type, which reduces the cost and operating costs of the solar water heating installation.

This study investigates a mirror-based reflectivity approach to mitigate shadow-induced power loss in building-integrated photovoltaics (BIPV). Experimental and simulation-based analyses reveal a near-linear relationship between shading area and efficiency loss: a 25% shaded area leads to over 20% reduction in PV performance. An optimal mirror-to-PV area ratio (20-30%) enhances daily irradiance by 46,5-161.3%. While BIPV systems on lower floors (1-6) suffer significant energy losses in winter, those above the 8th floor remain unaffected by shading. The findings provide an effective shading compensation strategy for BIPV deployment in high-density, high-latitude urban environments.

This paper presents the results of a study on the thermoelectric properties (electrical resistivity, Seebeck coefficient, and total thermal conductivity) of a composite with a p-type low-temperature thermoelectric Bi0,5Sb1,5Te3 matrix and inclusions of the semiconductor nickel ditelluride (NiTe2) as a filler. The studied composites were fabricated using solvothermal synthesis for the NiTe2 filler, and mechanochemical activation followed by spark plasma sintering for the Bi 0,5Sb1,5Te3 matrix and the composites themselves. It has been established that the introduction of 1 wt.% of NiTe2 into the composite matrix leads to a significant enhancement of the thermoelectric figure of merit (ZT) to 1,1 at 425 K, which is 16% higher compared to the matrix material itself (ZT ~ 0,95). This enhancement can be attributed to the effective phonon scattering at the NiTe2/Bi0,5Sb1,5Te3 interfaces, which leads to a reduction in the total thermal conductivity, while the power factor (S2/ρ) remains sufficiently high. A further increase in NiTe2 content to 2,5 and 5 wt.% leads to a degradation of ZT in the composites, which may be due to microstructural features such as the formation of a secondary phase of elemental tellurium. This phase forms «thermal bridges», thereby increasing thermal conductivity and slightly deteriorating the electronic transport properties.

The development of efficient thermoelectric materials for low-grade waste heat recovery is a critical challenge in modern energetics. In this study, bulk p-type nanocomposites based on the Bi0,5Sb1,5Te3 solid solution reinforced with reduced graphene oxide (rGO) nanosheets (concentrations of 1,0; 2,5 and 5,0 wt. %) were successfully fabricated. The synthesis approach combined high-energy ball milling for precursor homogenization and spark plasma sintering (SPS) for rapid consolidation. The impact of filler concentration on the microstructure evolution, phase composition, and transport properties was systematically evaluated in the 300-575 K temperature range.
Detailed microstructural analysis revealed that rGO inclusions are chemically inert and uniformly dispersed within the matrix. A key finding is the induction of a strong crystallographic texture during the SPS process: the 2D rGO sheets tend to align perpendicularly to the pressing direction, thereby blocking carrier transport along the parallel axis and inducing significant anisotropy in both electrical and thermal properties. Hall effect measurements confirmed that the hole concentration remained nearly constant (approx. 2,0 · 1019 cm-3) across all compositions, ruling out a doping effect. However, a sharp degradation in carrier mobility (decreasing from 267 to 83 cm2/V · s) was observed, attributed to severe scattering of charge carriers at the incoherent matrix/filler interfaces.
Conversely, the rGO network proved effective in scattering heat-carrying phonons, leading to a substantial reduction in total thermal conductivity (up to 23% reduction in the parallel direction compared to the pristine sample). Despite this beneficial thermal suppression, the deterioration of the electrical conductivity dominated the overall performance. Consequently, the peak dimensionless figure of merit (ZT) for the composites was lower than that of the unfilled matrix (ZT_max ≈ 1,0 at 420 K). This research highlights the critical trade-off between phonon blocking and electron transmitting mechanisms, suggesting that future strategies must focus on interface engineering to preserve carrier mobility in carbon-reinforced bismuth telluride thermoelectrics.

Based on the Russian Energy Development Strategy to 2050, the nuclear power industry faces the task of increasing flexibility by reducing load to 50% of its nominal capacity. A number of reasons are presented, leading to the conclusion that reducing NPP load is clearly unprofitable and ineffective. Therefore, a rationale is provided for providing NPPs with baseload power using a hydrogen complex through the electrolysis of hydrogen and oxygen, as a promising and competitive energy storage method. Thus, unused NPP capacity during the expected load reduction period is converted into hydrogen and oxygen for subsequent use to generate power during peak periods in the power grid. To achieve this, hydrogen is burned in oxygen in a special combustion chamber, and the resulting high-temperature steam is mixed with steam downstream of the steam generators and upstream of the NPP turbine. The main advantage of using a hydrogen complex is the ability to maintain the NPP’s nominal load (baseload mode) throughout the day. Crucially, the reactor operates at its nominal load. Based on forecast data, a significant increase in the commissioning of electrolysis capacity is noted for the period up to 2050. The authors have a solid scientific foundation in the problem of combining nuclear power plants with hydrogen complexes, having completed assessments of thermodynamic and technical-economic efficiency, as well as competitiveness indicators when compared with the benchmark option – pumped storage power plants. The article focuses on improving safety when using hydrogen to superheat the working fluid of NPP steam turbines due to the presence of unreacted hydrogen and oxygen after the combustion system, which entails the risk of forming an explosive mixture when entering the condenser. The authors previously published an article substantiating the principle of improving safety when using hydrogen in the cycle of NPP steam turbines. This article is a continuation of this work, aiming to theoretically evaluate the reduction in the proportion of unreacted hydrogen in a mixture with oxygen and superheated water vapor using a system for removing unreacted hydrogen based on catalytic recombination and magnetic separation, as well as to evaluate the efficiency of the unreacted hydrogen removal system based on an experimental model. The novelty of the proposed concept lies in its comprehensive principle of improving the safety of using hydrogen when it is burned in oxygen to superheat the working fluid of NPP steam turbines. The article analyzes the global state of the art in the field of catalytic hydrogen recombination, magnetic separation of various gas mixtures, as well as water electrolysis in a magnetic field and membrane hydrogen extraction. Using the example of a VVER nuclear power plant using hydrogen to superheat live steam from a steam turbine plant and the authors’ experience in experimentally studying the underburning of hydrogen during combustion in oxygen, an estimate is given of the possible proportion of unreacted hydrogen in the composition of the working fluid, which amounted to up to 2% by volume, depending on the number of hydrogen-oxygen combustion chambers. The paper presents a schematic diagram of the experimental setup, including a catalytic recombination and magnetic separation unit with a palladium membrane, and a methodology for evaluating the efficiency of the unreacted hydrogen removal system. The operating parameters of the experimental setup are presented. According to the experimental model, a mixture of superheated water vapor, hydrogen, and oxygen is passed through a recombination and magnetic separation unit operating under vacuum, which will lead to a decrease in the proportion of hydrogen in the mixture. The theoretical results of estimating the residual proportion of hydrogen in the mixture and the efficiency of the unreacted hydrogen removal system are presented. As shown by the performed assessments, the proposed system for removing unreacted hydrogen reduces its proportion in the mixture from 2 % vol. to 5,66 ∙ 10-3 % vol. at a pressure of 5 kPa, with the efficiency of the removal system amounting to 99,717%, and to 5,66 ∙ 10-4 % vol. at a pressure of 50 kPa with an efficiency of 99,972%. Thus, the increase in safety is achieved due to the fact that the mixture becomes very lean, since the hydrogen content is reduced by 2-3 orders of magnitude from the lower limit of ignition in a mixture with oxygen, which, with a tenfold reserve according to safety standards, is 0,4% by volume

To assess the survivability of an information system with a complex topology (the network graph is a forest or a hybrid structure containing fragments of radial, forest-shaped, ring-shaped, radial-ring and mesh topology) or a large dimension, it is proposed to use neural network analytical models as analytical support. An information system for assessing survivability is constructed and described, survivability criteria are identified, survivability in polynomial form is described, its calculation, and the results of calculating survivability polynomials are presented. A comparison of the model and actually calculated estimates of the survivability of the energy-saving management information system is carried out. A flow model of the survivability of an energy-saving management information system has been built.