Centrifugal compressor anti-surge control system modelling

<span>From the middle of XX century, natural gas is an important mineral, widely used in the energy sector. Transportation of natural gas is carried out via gas pipeline networks and compression stations. One of the key features which need to be implemented for any centrifugal gas compressor is a surge protection. This article describes the method and develops software application intended for simulation and study of surge protection system of a centrifugal compressor used in modern gas compression stations. Within the article research method, modelling environment’s block diagram, proposed algorithms and results are described. For surge cases control and prediction, Anti-surge control block implemented which based on practical experience and centrifugal compressor theory. To avoid complicated energy balancing differential equations the volumetric flow calculation algorithm proposed which is used in combination with Redlich-Kwong equation of state. Developed software’s adequacy test performed through modeling of one-stage gas compression scheme at rated speed with comparison of parameters with reference commercial software and verification of the anti-surge control system.</span>

Influence of Wind Speed Forecasting Error on the Choice of the Number of Balancing System Batteries

In the energy balancing system of distributed generation systems with RES (renewable energy sources), in particular with wind turbines, the effective use of the battery of the balancing system depends on the charge-discharge modes that are implemented. To be effectively used in an energy balancing system, the RES control system should coordinate the processes of energy generation and accumulation in the system through the implementation of operational management with forecasting. Depending on the characteristics of the battery and the accuracy of the measurement or prediction of the energy the battery capacity (or the number of batteries) that will provide the specified control range (controlled operation area) needs to be chosen. Empirical relations (equations) devoted to the dependence of the battery capacity on the discharge current and to the change of voltage at the terminals of the battery during direct current discharge were listed. Among the equations Peukert’s law was chosen. A general view of the dependence of the battery capacity on the discharge current was shown. The formula for Peukert's constant (coefficient) was given. 5 Packert's law limitations were listed including the fact that the effect of temperature on the battery is not taken into account. The influence of depth charge-discharge and the number of discharge cycles on the capacitance was shown. In the process of using the battery and increasing the number of charge-discharge cycles, the capacity decreases. Peukert’s formula was extended to be influenced by temperature: both the Peukert’s capacity and the Peukert’s coefficient depend on the temperature because the Peukert’s coefficient depends on the capacity. For further calculations, a rechargeable battery HZB12-180FA from manufacturer HAZE Battery Campany Ltd was chosen. The temperature was taken into account by empirical dependences from the manufacturer and then they were approximated by 3rd order polynomials. Graphical results of the approximation were shown. The formula of dependency between the power of the wind turbine and the wind speed was shown. The connection between wind speed prediction error, amount of power that could not be obtained because of that and the number of batteries that would provide the specified control range (controlled operation area) was shown. Thus, for calculation of the number of batteries the depth of discharge, temperature and prediction (measurement) error were taken into account. Example dependences of the number of batteries on the wind speed error at temperatures of -20 °C, 0 °C and 20 °C were shown. Curves of dependence of the number of batteries of the balancing system on the ambient temperature and the error of wind speed forecasting was constructed. As an example, when the prediction error increases from 10% to 15%, the number of batteries needs to be increased by 1.17 times, and when the temperature decreases from 20 °C to 0 °C, the number of batteries needs to be increased by 1.48 times. The results of the work can be used at the stage of planning the wind turbine when choosing the number and capacity of the batteries to be installed. Possible areas of further research are using Peukert's formulas, generalized for other or different types of batteries, using other formulas, except for Peukert’s one, for taking into account the dependence of battery capacity on discharge current, using a non-empirical approach to include dependency on temperature.

Resonant passive energy balancing of morphing helicopter blades with bend–twist coupling

With increasing demand for rotor blades in engineering applications, improving the performance of such structures using morphing blades has received considerable attention. Resonant passive energy balancing (RPEB) is a relatively new concept introduced to minimize the required actuation energy. This study investigates RPEB in morphing helicopter blades with lag–twist coupling. The structure of a rotating blade with a moving mass at the tip is considered under aerodynamic loading. To this end, a three-degree-of-freedom (3DOF) reduced-order model is used to analyse and understand the complicated nonlinear aeroelastic behaviour of the structure. This model includes the pitch angle and lagging of the blade, along with the motion of the moving mass. First, the 3DOF model is simplified to a single-degree-of-freedom model for the pitch angle dynamics of the blade to examine the effect of important parameters on the pitch response. The results demonstrate that the coefficient of lag–twist coupling and the direction of aerodynamic moment on the blade are two parameters that play important roles in controlling the pitch angle, particularly the phase. Then, neglecting the aerodynamic forces, the 3DOF system is studied to investigate the sensitivity of its dynamics to changes in the parameters of the system. The results of the structural analysis can be used to tune the parameters of the blade in order to use the resonant energy of the structure and to reduce the required actuation force. A sensitivity analysis is then performed on the dynamics of the 3DOF model in the presence of aerodynamic forces to investigate the controllability of the amplitude and phase of the pitch angle. The results show that the bend–twist coupling and the distance between the aerodynamic centre and the rotation centre (representing the direction and magnitude of aerodynamic moments) play significant roles in determining the pitch dynamics.

T-shaped hybrid alternate arm converter with arm energy balancing control for battery energy storage systems

Multilevel voltage source converters (VSCs), such as modular multilevel converter (MMC), cascaded H-Bridge (CHB) and alternate arm converter (AAC), are competent topologies for battery energy storage systems (BESSs) due to modularity, scalability and low harmonic distortion. However, there is a lack of studies about interfacing AAC with a BESS due to the arm energy balancing issue. Redundant sub-modules (SMs) are inserted passively into MMC, CHB and AAC to achieve high reliability; consequently, some of them are constantly idling, resulting in low SM utilization. We propose a novel topology -T-shaped hybrid alternate arm converter (TSHAAC) for BESS applications. In addition to the aforementioned features, the proposed TSHAAC requires lower number of SMs than MMC and AAC, along with lower number of switches than CHB. Moreover, an adapted arm energy balancing control is proposed to take advantage of the redundant SMs that are idling to achieve faster balancing than in conventional AAC configuration. The simulation results validate the integration of TSHAAC configuration in a BESS; the adapted arm energy balancing control is able to improve the balancing duration by 27 %.

Efficient Energy Balancing Across Multiple Harmonics of Nonlinear Normal Modes

Predicting the forced responses of nonlinear systems is a topic that attracts extensive studies. The energy balancing method considers the net energy transfer in and out of the system over one period, and establishes connections between forced responses and nonlinear normal modes (NNMs). In this paper, we consider the energy balancing across multiple harmonics of NNMs for predicting forced resonances. This technique is constructed by combining the energy balancing mechanism with restrictions (established via excitation scenarios) on external forcing and harmonic phase-shifts; a semi-analytical framework is derived to achieve both accurate/robust results and efficient computations. With known inputs from NNM solutions, the required forcing amplitudes to reach NNMs at resonances, along with their discrepancy, i.e. the harmonic phase-shifts, are computed via a one-step scheme. Several examples are presented for different excitation scenarios to demonstrate the applicability of this method, and to show its capability in accurately predicting the existence of an isola where multiple harmonics play a significant part in the response.