Bulletin of the Polish Academy of Sciences Technical Sciences

In this paper, a control strategy for real-time operation of a master-slave controlled microgrid is developed. The basic idea of this control strategy is to schedule all dispatchable energy sources available into a microgrid to minimize its operational costs. Control actions are centrally evaluated by solving a two-stage optimization problem formulated to take place on two different time-scales: in the day-ahead and in the real-time. The first one provides a 24-hour plan in advance. It mainly draws up the active power levels that Distributed Energy Resources (DERs) should provide for each quarter hour of the next day by taking into account energy prices of the day-ahead energy market, the forecasted energy production of non-dispatchable renewables and loads. The real-time optimization problem updates the active power set-points of DERs in order to minimize as much as possible the real-time deviations between the actual power exchanged with the utility grid and its scheduled value. The effectiveness of the proposed methodology has been experimentally tested on an actual microgrid.

The paper raises the issue of optimizing the control of the rural low voltage microgrids. Microgrids can operate in a synchronous mode with grids of distribution system operators and in an island mode. We can distinguish two control strategies in microgrids: one approach based on centralized control logic, which is usually used, and another on decentralized control logic. In this paper we decided to present the approach based on the distributed control, combining the efforts of the distributed cooperative control and modified Monte Carlo optimization method. Special attention has been paid to the impact of the order of processing particular devices’ groups on results of optimization calculations. Moreover, different scenarios of behavior of the microgrid control system with respect to the communication loss have been also presented. The influence of the issue of continuity of communication between particular devices’ groups on the possibility of carrying out the optimization process has been investigated. Additionally, characteristics of power loads and generation of electricity from small renewable energy sources appearing in rural areas have been described and the sensitivity of the optimization algorithm to the changes of demanded power values and changes of values of power generated by renewable energy sources has been studied. We analyzed different objective functions which can be used as an optimization goal both in synchronous and island operation modes of microgrid. We decided to intensively test our approach on a sample rural LV microgrid, which is typical in the countryside. The observed results of the tests have been presented and analyzed in detail. Generally, results achieved with the use of proposed distributed control are the same as with the use of centralized control. We think that the approach based on distributed control is promising for practical applications, because of its advantages.

Three synchronous machine models representing three precision levels (complete, reduced and static), implemented in a virtual synchronous generator (VSG)-based industrial inverter, are compared and discussed to propose a set of tests for a possible standardization of VSG-based inverters and to ensure their “grid-friendly” operation in the context of isolated microgrids. The models and their implementation in the microcontroller of an industrial inverter (with the local control) are discussed, including the usability of the implementation with large-scale developments constraints in mind. The comparison is conducted based on existing standards (for synchronous machines and diesel generators) in order to determine their needed evolution, to define the requirements for future grid-friendly inverter-based generators, notably implementing a VSG solution.

Software power protection tester implemented in a real-time operating system (RTOS) might replace the conventional testing setups in IEC 61850 protection systems. This paper describes an open power protection testing platform. Linux RT capabilities related to runtime environment for such a tester are examined and OS latency sources are identified and evaluated. An algorithm for a multithreaded tester operation is proposed, including Sampled Values (SV) publisher, GOOSE input/output and time synchronization. SV and GOOSE services implemented in RT Linux environment are evaluated in accordance with IEC 61850‒5 transfer time requirements. Linux PTP time synchronization service of two similar systems controlling its electrical ports is evaluated in different synchronization scenarios. The developed tester is compared to an equivalent conventional setup during the test of IED over-current function. The conducted tests show that the Linux implementation of power protection tester in the case of scheduler latency, time synchronization accuracy and transfer time all meet the requirements of IEC 61850.

This paper discusses three variants of how e-mobility development will affect the Polish Power System. Multivariate forecasts of annual new registrations of electric vehicles for up to seven years are developed. The forecasts use the direct trend extrapolation methods, methods based on the deterministic chaos theory, multiple regression models, and the Grey model. The number of electric vehicles in use was determined for 2019‒2025 based on the forecast new registrations. The forecasts were conducted in three variants for the annual electric energy demand in 2019‒2025, using the forecast number of electric vehicles and the forecast annual demand for electric energy excluding e-mobility. Forecasts were conducted in three variants for the daily load profile of power system for winter and summer seasons in the Polish Power system in 2019‒2025 based on three variants of the forecast number of electric vehicles and forecast relative daily load profiles.

Lighting technologies developed significantly in the last decade. New LED light sources, dedicated luminaires and improved lighting control techniques gave rise to new possibilities in improving energy efficiency of lighting solutions. The article is an overview of interior, road and exterior architectural object lighting design strategies. It also presents design considerations that directly impact lighting conditions and energy efficiency. Practical examples of the application of basic design strategies, accompanied by the obtained energy results, are also depicted. Issues discussed in the article may be useful in researching and designing interior and road lighting, as well as floodlighting. They can also be useful in planning and implementing strategies aimed at improving lighting conditions and energy efficiency of lighting solutions.

Nowadays the demand for renewable energy sources is constantly growing. There are several reasons of such state, including requirements for energy-efficient new buildings and reduction of greenhouse gas emissions. An exemplary solution that may help to reduce “traditional” primary energy consumption is local energy source utilization. The article presents a simplified feasibility study of hybrid energy system under Polish law and economic conditions for a self-government unit, that is legally obliged to apply means of energy efficiency improvement. The aim of this paper is to provide a simple algorithm to find optimal hybrid PV and wind power source sizing for a prosumer. Resource data used in analyses are imported from Photovoltaic Geographical Information System and cover a period of one year. The paper includes two different methodologies applied to solve the problem of optimal hybrid energy system sizing. The first approach is heuristic and based on monthly energy balancing while the second is iterative and takes into account hourly energy balance. The results from both methods are compared and verified by HomerPro software, that shows significant differences between two algorithms. At the end economic assessment based on Net Present Value method is performed.

The paper proposes to apply an algorithm for predicting the minimum level of the state of charge (SoC) of stationary supercapacitor energy storage system operating in a DC traction substation, and for changing it over time. This is done to insure maximum energy recovery for trains while braking. The model of a supercapacitor energy storage system, its algorithms of operation and prediction of the minimum state of charge are described in detail; the main formulae, graphs and results of simulation are also provided. It is proposed to divide the SoC curve into equal periods of time during which the minimum states of charge remain constant. To predict the SoC level for the subsequent period, the learning algorithm based on the neural network could be used. Then, the minimum SoC could be based on two basic types of data: the first one is the time profile of the energy storage load during the previous period with the constant minimum SoC retained, while the second one relies on the trains’ locations and speed values in the previous period. It is proved that the use of variable minimum SoC ensures an increase of the energy volume recovered by approximately 10%. Optimum architecture and activation function of the neural network are also found.

This paper presents modern methods for designing optical systems for luminaires in the context of long years of light sources development. It shows that the development of technology for producing increasingly precise optical systems has led to an evolution in the construction of luminaires with increased efficacy and utilizing more efficiently the features of a specific family of light sources. Methods for designing and modelling optical systems with the use of mathematical curves as well as advanced the free-forming method are described. The paper also shows methods for modelling light sources features, especially luminance ones, designed to make precise simulation calculations required in any luminaire design process. Knowledge of luminance distributions of light sources and precise luminance distributions of optical systems for luminaires raises the design process to a very high level, enabling positive modern light source features, such as high luminance and their small dimensions, to be used consciously while minimizing negative ones, such as discomfort glare, caused by luminaires. The paper presents the results of simulation calculations and laboratory measurements for a selected case of luminaire equipped with a discharge lamp of maximum luminance exceeding 30 million cd/m².

Functional properties of some electrical devices are expressed in the form of a dependence between parameters defining a given aspect of device duty or work circumstance (e.g. breakdown voltage): contacts distance for a circuit breaker, current (voltage for voltage limiters or reaction time), and load current for over current protection. Such characteristics are obtained experimentally, usually in a set of test series, each performed with a fixed independent parameter. Results of each series generate sets of data for estimation of statistical properties of a dependent parameter: distribution, expected value, variance and confidence interval. These statistics concern one point of the tested characteristic, so to get data of it as a whole, that would satisfy the needs for designing an electrical system, a large number of tests can be necessary. The way to reduce the number of tests may consists in: defining the characteristic not as a series of points, but as an analytical function with some specific parameters. This can be combined with aggregation of results of all tests in one set of data for estimation of statistical properties of the mentioned parameter. This paper presents an application of the above approach to tests of time-current characteristics of fuses.

Short-term contact losses between a pantograph and a contact wire are not included in the standards nor are they taken into account in evaluating pantograph-contact wire interaction. These contact losses, however, accelerate wear and tear as well as disturb operation of vehicles’ drive systems. The article presents the effects of short-term contact breaks as well as an analysis of impact of contact breakages on a vehicle’s current at 3 kV DC power supply. Results of voltage and current oscillations measured in real conditions when pantograph of a DC driven chopper vehicle was running under isolators were presented. Then a simulation model of a vehicles with ac motors and voltage inverters was derived to undertake simulation experiments verifying operation of such a vehicle in condition similar to those measured in real condition.

The aim of the presented work was to examine the reliability assessment model on the example of a selected power grid object. The analyzed object was tested based on assumptions about technological breaks that were caused by overvoltage, among others. The study was conducted to check the reliability of integral elements of the power grid object and to assess the change in reliability level as a function of the frequency of inspections. The test results are to determine the optimal frequency of inspections of individual power grid objects in order to increase its reliability. In addition, the possibility of correlating optimal inspection periods resulting from the findings of this paper with periodic inspections of power network facilities was assessed.

The article is a continuation of a study on the synthesis of matching multi-terminal networks, also known as compensators. The reactive four-terminal-network compensators for linear loads were introduced in previous publications, but it appeared that they operate effectively with nonlinear loads too. The methods to create a compensator for a mono-harmonic source, which allows complete independence of input from output waveforms, ensuring optimal operating conditions for the source, are presented herein. The work for the first time presents the optimal four-terminal-network compensator applied to a nonlinear load.

This paper describes practical issues related to control of the active power buffer (APB) developed for a 2 kVA single-phase inverter. The buffer is designed using the latest GaN HEMTs controlled with triangular current mode to reduce switching losses, however, the switching frequency should be limited to 1 MHz. In the case of the presented analogue-digital controller, frequency is influenced by a reference current of the APB and circuit. Therefore, the operation at start-up and shut-down is especially challenging. A modified control algorithm that also includes pre-charging and discharging process of the energy buffer is presented and experimentally verified by series of tests of the 2 kVA GaN based inverter with the APB.

The increased power density, reduced switching losses with minimum electromagnetic interference (EMI), and high efficiency are essential requirements of power converters. To achieve these characteristics, soft power converters employing soft switching techniques are indispensable. In this paper, a ZCS/ZVS PWM AC/DC converter topology has been emphasized, which finds applications in high power systems such as automobile battery charging and renewable energy systems. This converter scheme maintains zero current and zero voltage switching conditions at turn on and turn off moments of semiconductor switches, respectively and soft operation of rectifier diodes that lead to negligible switching and diode reverse recovery losses. Moreover, it improves power quality and presents high input power factor, low total harmonic distortion of the input current (THDI) and improved efficiency. The validity of theoretical analysis of the proposed converter has been carried out experimentally on a 10 kW laboratory prototype. Experimental results prove that the soft switching operation of the semiconductor switches and diodes is maintained at 98.6% rated load efficiency. In addition, the performance evaluation has been performed by comparative analysis of the proposed converter with some prior art high power AC/DC converters. Efficiencies of the proposed and prior art high power topologies have been determined for different load conditions. The highest efficiency, power factor and lower THDI of the proposed converter topology complies with international standards.

The development of technology and design of light management systems remains dynamic. Among all the benefits offered by these systems, the most valuable might definitely be the possibility of saving energy consumption. Knowing the value of energy savings is the key factor that users need to know before deciding to use a lighting management system (the type of light management system). For this purpose, it is useful to simulate the operation of the lighting control system, for example in the DIALux program. Such simulation helps evaluate potential savings in electricity consumption using the proposed lighting control system. In the DIALux program, it is possible to change the luminous flux value of luminaires. In such a case, it becomes possible to semi-simulate the light management system’s operation as we don’t receive actual information on reducing installed power of the lighting system during reduction of the luminous flux value of luminaires. This article shows what type of technical data are important to use for the DIALux program to properly and accurately simulate light management systems and to receive accurate data on energy saving. It also presents the results of photometrical and electric parameter measurements (Φ – luminous flux, P – power, PF – power factor, THDi – total harmonic distortion of current). The article discusses the power control characteristics obtained on the basis of these measurements and explores the source of differences between simulation of energy saving calculations and real measured energy savings. An existing lighting control system installed in an office reception area was used to compare calculations with the real value of energy consumption reduction. The impact of electronic power and control systems on electrical network parameters is also an important problem mentioned in this article. It also explores the effect of power regulation of LED luminaires and LED modules on the value of the power factor and total harmonic distortion (current) value (THDi).

Thanks to a very high luminous efficacy of LED lamps (over 160 lm/W) they are the most preferred light sources in lighting applications today. The useful lifetime of LED modules exceeds 50,000 hours. Chromatic parameters of lamps making use of SSL (Solid State Lighting) have already equalled classic solutions, although they were noticeably worse not so long ago. High values of the Colour Rendering Index (CRI) and ease of control over the luminous flux cause that lamps with LEDs have become very attractive solutions. Today, the most important problem concerns LED drivers supplied from the 230 VAC mains. The lifetime of switched-mode converters, including electrolytic capacitors, is considerably shorter than that of LEDs. This paper discusses the features of alternative drivers for LED modules which are supplied directly from the 230 VAC mains and do not contain any electrolytic capacitors. In particular, power factor and efficiency of lamps with one or two LED strings are analysed and some hints concerning optimal design of such lamps are given. A unique feature of this work is a detailed analysis of harmonics contents in the supply current of such drivers, proving their conformity with the relevant standard. Finally, some problems associated with flicker resulting from the considered type of supply are mentioned.

In this study, an energy-based spectrum sensing method combined with copula theory is proposed for cognitive radio systems. In the proposed spectrum sensing model, cognitive radio users first make their own local spectrum decision with energy-based spectrum sensing. Then, they forward their decision to the fusion center. In the fusion center, this decision is compared with the threshold value determined by copula theory and global spectrum decision is made. The test statistic at the fusion center were obtained with the Neyman Pearson approach. Thus, the fusion rule was created for the fusion center and necessary simulation studies were performed. According to the results of the simulation studies, the proposed detection method showed better results than the traditional energy based detection method.

Digital system algorithms such as FFT algorithms, convolution, image processing algorithm, etc. deploy Multiply and Accumulate (MAC) unit as an evaluative component. The efficiency of a MAC typically relies on the speed of operation, power dissipation, and chip area along with the complexity level of the circuit. In this research paper, a power-delay-efficient signed-floating-point MAC (SFMAC) is proposed using Universal Compressor based Multiplier (UCM). Instead of having a complex design architecture, a simple multiplexer-based circuit is used to achieve a signed-floating output. The 8£8 SFMAC can take 8-bit mantissa and 3-bit exponent and therefore, the input to the SFMAC can be in the range of –(7.96875)₁₀ to +(7.96875)₁₀. The design and implementation of the proposed architecture is executed on the Cadence Spectre tool in GPDK 90 nm and TSMC 130 nm CMOS, which proves as power and delay efficient.

In the past decade, there has been significant progress in development of the colloidal quantum dot (CQD) photodetectors. The QCD’s potential advantages include: cheap and easy fabrications, size-tuneable across wide infrared spectral region, and direct coating on silicon electronics for imaging, which potentially reduces array cost and offers new modifications like flexible infrared detectors. The performance of CQD high operating temperature (HOT) photodetectors is lower in comparison with detectors traditionally available on the global market (InGaAs, HgCdTe and type-II superlattices). In several papers their performance is compared with the semiempirical rule, “Rule 07” (specified in 2007) for P-on-n HgCdTe photodiodes. However, at present stage of technology, the fully-depleted background limited HgCdTe photodiodes can achieve the level of room-temperature dark current considerably lower than predicted by Rule 07. In this paper, the performance of HOT CQD photodetectors is compared with that predicted for depleted P-i-N HgCdTe photodiodes. Theoretical estimations are collated with experimental data for both HgCdTe photodiodes and CQD detectors. The presented estimates provide further encouragement for achieving low-cost and high performance MWIR and LWIR HgCdTe focal plane arrays operating in HOT conditions.

The paper presents a concept of the vehicle/road infrastructure in vehicle-to-infrastructure (V2I) communication for tagging and informing vehicles about the surrounded environment. A frame analysis and the influence of the data packet size on Ultra-wideband (UWB) were investigated. The authors have determined the distance that could be traveled by a vehicle at the given speed in relation to the amount of data that has to be transmitted during the ranging procedure. The authors propose a data frame format (using the IEEE 802.15.4a protocol) for coding/encoding the information about the road infrastructure efficiently during the positioning procedure. It affects to minimum the time that is required to exchange messages during the ranging and communication process. The whole system is an efficient and reliable element that enhances/extends the existing components of advanced driver-assistance systems (ADAS), which will facilitate validation of the information obtained from devices such as lidar, radar or video. The impact of the transmitted payload to the distance traveled by car opens the door to future research on the possibility of implementing efficient vehicle-to-vehicle (V2V) communication for autonomous driving or and other smart city solutions.

The problem of performing software tests using Testing-as-a-Service cloud environment is considered and formulated as an~online cluster scheduling on parallel machines with total flowtime criterion. A mathematical model is proposed. Several properties of the problem, including solution feasibility and connection to the classic scheduling on parallel machines are discussed. A family of algorithms based on a new priority rule called the Smallest Remaining Load (SRL) is proposed. We prove that algorithms from that family are not competitive relative to each other. Computer experiment using real-life data indicated that the SRL algorithm using the longest job sub-strategy is the best in performance. This algorithm is then compared with the Simulated Annealing metaheuristic. Results indicate that the metaheuristic rarely outperforms the SRL algorithm, obtaining worse results most of the time, which is counter-intuitive for a metaheuristic. Finally, we test the accuracy of prediction of processing times of jobs. The results indicate high (91.4%) accuracy for predicting processing times of test cases and even higher (98.7%) for prediction of remaining load of test suites. Results also show that schedules obtained through prediction are stable (coefficient of variation is 0.2‒3.7%) and do not affect most of the algorithms (around 1% difference in flowtime), proving the considered problem is semi-clairvoyant. For the Largest Remaining Load rule, the predicted values tend to perform better than the actual values. The use of predicted values affects the SRL algorithm the most (up to 15% flowtime increase), but it still outperforms other algorithms.

The model predictive control (MPC) technique has been widely applied in a large number of industrial plants. Optimal input design should guarantee acceptable model parameter estimates while still providing for low experimental effort. The goal of this work is to investigate an application-oriented identification experiment that satisfies the performance objectives of the implementation of the model. A- and D-optimal input signal design methods for a non-linear liquid two-tank model are presented in this paper. The excitation signal is obtained using a finite impulse response filter (FIR) with respect to the accepted application degradation and the input power constraint. The MPC controller is then used to control the liquid levels of the double tank system subject to the reference trajectory. The MPC scheme is built based on the linearized and discretized model of the system to predict the system’s succeeding outputs with reference to the future input signal. The novelty of this model-based method consists in including the experiment cost in input design through the objective function. The proposed framework is illustrated by means of numerical examples, and simulation results are discussed.

This paper presents an approach to the construction and measurements of electrodynamic and reluctance actuators. Executive elements were used as drives in a novel concept of a magnetomotive micropump. The paper discusses various aspects concerning the designation of parameters, control system, the explanation of physical phenomena, and the optimization of the basic elements for coil units. The conducted work describes the measurement system and the analysis of the derived values. The actuators were compared and the pros/cons of building the conceptual device were highlighted. The best solution to be used in the upcoming work concerning the construction of a magnetomotive micropump was chosen based on measurements, engineering aspects, layout control, and key parameters such as the piston velocity, energy stored in capacitors, and efficiencies.

The presented results describe the effect of severe plastic deformation on the structure and mechanical properties of AA5083 and AA5754 alloys. Both materials were subjected to single hydrostatic extrusion (HE) and cumulative hydrostatic extrusion in the case of AA5083 and a combination of plastic deformation by equal-channel angular pressing (ECAP) with the next HE for AA5754. After the deformation, both alloys featured a homogeneous and finely divided microstructure with average grain size deq = 140 nm and 125 nm for AA5083 and AA5754, respectively. The selection of plastic forming parameters enabled a significant increase in the UTS tensile strength and YS yield stress in both alloys – UTS =  510 MPa and YS = 500 MPa for alloy AA5083 after cumulative HE, and 450 MPa and 440 MPa for alloy AA5754 after the combination of ECAP and HE, respectively. It has been shown on the example of AA5083 alloy that after the deformation the threads of the fasteners made of this material are more accurate and workable at lower cutting speeds, which saves the cutting tools. The resultant properties of AA5083 and AA5754 alloys match the minimum requirements for the strongest Al-Zn alloys of the 7xxx series, which, however, due to the considerably lower corrosion resistance, can be replaced in many responsible structures by the AA5xxx series Al-Mg alloys presented in this paper.

The paper evaluates the causes related to the fatigue damage in a conveyor slide plate, exposed to high-frequency cyclic loads. The plate was made of 1.4301 acid-resistant steel. The fractography showed that the plate failure was caused by fatigue crack. A nonlinear analysis of plate deformation was conducted using the finite element method (FEA) in LS-Dyna software. The maximum normal stresses in the plate fracture were used in further analysis. A “fatigue limit” calculated initially using a FITNET procedure was above the maximum stress calculated using FEA. It indicates that the structural features of the plate were selected correctly. The experimental test results for 1.4301 acid-resistant steel were described using a probabilistic Weibull distribution model. Reliability was determined for the obtained S-N curve at 50% and 5% failure probability allowing for the selected coefficients (cycle asymmetry, roughness, variable load) and the history of cyclic loading. Cumulative damage was determined using the Palmgren-Miner hypothesis. The estimated fatigue life was similar to the actual value determined in the operating conditions for the S-N curve at 5% failure probability. For engineering calculations, the S-N curve at max. 5% failure probability is recommended.

Among rapid development of wireless communication, technology cryptography plays a major role in securing the personal information of the user. As such, many authentication schemes have been proposed to ensure secrecy of wireless communication but they fail to meet all the required security goals. The proposed signcryption scheme uses multi-factor authentication techniques such as user biometrics, smart card and passwords to provide utmost security of personal information. In general, wireless devices are susceptible to various attacks and resource constraint by their very nature. To overcome these challenges a lightweight cryptographic scheme called signcryption has evolved. Signcryption is a logical combination of encryption and digital signature in a single step. Thereby it provides necessary security features in less computational and communication time. The proposed research work outlines the weaknesses of the already existing Cao et al.’s authentication scheme, which is prone to biometric recognition error, offline password guessing attack, impersonation attack and replay attack. Furthermore, the proposed study provides an enhanced multi-factor authentication scheme using signcryption based on hyper elliptic curve cryptography and bio-hash function. Security of the proposed scheme is analyzed using Burrows-Abadi-Needham logic. This analysis reveals that the proposed scheme is computational and communication-efficient and satisfies all the needed security goals. Finally, an analysis of the study results has revealed that the proposed scheme protects against biometric recognition error, password guessing attack, impersonation attack, DoS attack and dictionary attack.

The existing traffic noise prediction models in road intersections relate mainly to the typical solutions of intersection geometry and traffic organisation. There are no models for large and more complex intersections such as signalised roundabouts. This paper presents the results of studies on the development of a traffic noise prediction model for this type of intersection. The model was developed using a multiple regression method based on the results of field measurements of traffic parameters and noise levels in the vicinity of signalised roundabouts in Poland. The obtained model consists of two groups of variables affecting noise levels at the intersection. The first group determines in detail the influence of traffic and geometry of the closest entry. The second group shows the influence of more distant noise sources (traffic at the three remaining entries of the intersection) and the influence of the dimensions of the entire intersection. The developed model was verified through additional field measurements, as well as compared to the results of two methods of traffic noise prediction: the French ‘NMPB-Routes-2008’ and the German ‘RLS-90’. The obtained results confirmed a higher accuracy of calculations performed using the developed model in the range of: −1.2 dB ÷ +1.0 dB, while the ‘NMPB-Routes-2008’ and ‘RLS-90’ calculate precision were respectively: −2.8 dB ÷ +1.3 dB, and +0.8 dB ÷ +5.2 dB. Therefore, the developed model allows for a more accurate prediction of noise levels in the vicinity of signalised roundabouts in a flat terrain without buildings and noise barriers.

One of the little described problems in hydrostatic drives is the fast changing runs in the hydraulic line of this drive affecting the nature of the formation and intensity of pressure pulsation and flow rate occurring in the drive. Pressure pulsation and flow rate are the cause of unstable operation of servos, delays in the control system and other harmful phenomena. The article presents a flow model in a hydrostatic drive line based on fluid continuity equations (mass conservation), maintaining the amount of Navier-Stokes motion in the direction of flow (x axis), energy conservation (liquid state). The movement of liquids in a hydrostatic line is described by partial differential equations of the hyperbolic type, so modeling takes into account the wave phenomena occurring in the line. The hydrostatic line was treated as a cross with two inputs and two outputs, characterized by a specific transmittance matrix. The product approximation was used to solve the wave equations. An example of the use of general equations is presented for the analysis of a miniaturized hydrostatic drive line fed from a constant pressure source and terminated by a servo mechanism.