Unstable Operating Region Research Articles

Flexible operation, optimisation and stabilising control of a quench cooled ammonia reactor for power-to-ammonia

This paper discusses the operation of an ammonia reactor for a Power-to-Ammonia (P2A) plant. We develop a dynamic model for an ammonia reactor system consisting of a three-bed quench cooled adiabatic reactor and a feed-effluent heat exchanger. The reactor bed model is formulated as a differential algebraic equations (DAE) system. We use the thermodynamic software Thermolib for rigorous modelling of the thermodynamic functions in the high pressure ammonia reactor. We present a case study of an ammonia synthesis loop in a P2A plant connected to a 250 MW renewable energy source with a capacity factor of 0.4. Static optimisation and stability analysis are performed for the reactor system, which located the optimal operating point close to instability. The dynamic simulations confirm the unstable operating regions as severe oscillations arise. A fluctuating energy supply from renewable sources requires the ammonia reactor to operate over a wide operating window from 20%–120% of nominal capacity. We formulate a realistic strategy for varying the supply of H2 and N2 (load) to the synthesis loop depending on the available energy. Open-loop simulations show that varying the synthesis feed flow cause oscillations in the ammonia reactor system. Therefore, we propose a regulatory control structure for stabilising the ammonia reactor. The optimisation algorithm determines the reactor set-point state by updating at changes to the synthesis loop load. Hereby, we achieved fast control and close tracking of the set-points for the ammonia reactor.

Converter-driven stability constrained unit commitment considering dynamic interactions of wind generation

With increasing penetration of renewable energy in power systems, conventional unit commitment (UC) focusing on static constraints may fail to meet dynamic constraints, such as converter-driven stability. This paper proposes a practical paradigm to perform UC considering the requirement of converter-driven stability in wind generation penetrated power systems. First, wind generation is regarded as a constant source, and a regular UC problem is solved without considering the dynamic impact of wind generation. Second, converter-driven stability analysis is employed to evaluate the stability margin of the UC solution. Different wind penetration levels and dynamic interaction conditions are investigated to account for the dynamic impact of wind generation. In several time horizons, especially heavy loading periods, the stability margin may be very limited or negative, and a modification to the UC solution should be carried out. Thus, a power sensitivity-based power dispatch method is elaborated to enhance the stability margin as well as update the UC solution. It is substantiated that in strong interaction cases, the system has more unstable operating regions (e.g., 1.33 times of those in weak interaction cases) and greatly affects the feasibility of the UC solution, but can be effectively tackled with the proposed power dispatch method.

Design of PI controller parameters of a CSI‐fed SCIM drive ensuring high damping ratio and maximum system stability

AbstractThe control scheme for an electric motor drive is generally implemented by involving proportional‐integral (PI) controllers in current and speed feedback control loops. A good design of PI controller parameters has always been a challenging task for control system design engineers. This paper describes the D‐decomposition method for the design of the parameters of involved DC‐link current and speed PI controllers in closed‐loop scheme of a pulse width‐modulated, current source inverter (CSI)‐fed squirrel‐cage induction motor drive. The PI controllers ensure the stable operation of CSI‐fed induction motor in natural unstable operating region of its torque‐slip characteristic. In order to achieve smoother speed tracking performance with minimum overshoot/undershoot, the damping ratio has been pre‐specified while designing the PI controller parameters using the D‐decomposition method. Simulation results have been presented to confirm the design and have been compared with the results already published.

Limitations of autopilot design for controlling a statically unstable flexible interceptor

The Mach number, angle of attack and altitude of operation for an interceptor vary widely during the course of its trajectory. As a result, the interceptor Center of Pressure (CP) locations move significantly around a given Center of Gravity (CG) location at these operating conditions. This results in an inevitable variation in aerodynamic static stability leading to stable and unstable operating regions. In order to ensure good speed of response during the interceptor homing phase, lesser static stability is desirable. Hence the requirement to handle aerodynamic instability at some other operating conditions in the interceptor envelope become inevitable. Since flexibility has a strong bearing on autopilot design, it becomes necessary to control unstable operating points in the presence of flexibility modes. Despite the static stability variation, aerodynamic design can control the level of maximum instability of the configuration. Hence the maximum static instability the autopilot can handle has to be specified for aerodynamic configuration design. This paper brings out the limitations of autopilot design in controlling an unstable interceptor with low bending mode frequencies in terms of maximum instability the autopilot design can handle, which serves as an important input for aerodynamic design.

A parametric study of an unbalanced Jeffcott rotor supported by a rolling-element bearing

Rolling-element bearings are widely used in industrial rotating machines, and hence there is a strong need to accurately predict their influence on the response of such systems. However, this can be challenging due to an interaction between the dynamics of the rotor and the bearing nonlinearities, and it becomes difficult to provide a physical explanation for the nonlinear response. A novel approach, combining a Jeffcott rotor supported by a detailed bearing model with the generalised harmonic balance method, is presented, enabling an in-depth study of the complex rotor–stator interaction. This allows the quasi-periodic response of the rotor, due to variable compliance, to be captured, and the impact of clearance, ring and stator compliance, and centrifugal loading of the bearing on the response to be investigated. A strongly nonlinear response was observed due to the bearing, leading to large shifts in frequency as the excitation amplitude was increased, and the emergence of stable and unstable operating regions. The variable compliance effect generated sub-synchronous forcing, which led to sub-resonances when the ball pass frequency coincided with the frequency of one of the modes. Radial clearance in the bearing had by far the largest influence on the unbalance response, the self-excitation due to variable compliance, and the stability. Introducing outer ring compliance was found to slightly soften the system, and centrifugal loading on the bearing elements marginally increased the system’s region of instability, but neither of these effects had a significant impact on the response for the investigated bearing. When the bearing was mounted on a sufficiently compliant stator, the system was found to behave linearly.

Analysis and study of two‐dimensional parameter bifurcation of wind power farms and composite loads

AbstractThis study focuses on the stability of power system based on codimension‐two bifurcation theory. In this paper, we investigate the impact of load modeling on permissible wind power generation margins in distribution networks. The study considers codimension‐two bifurcations of equilibria and limit cycles in wind power systems depending on varying two parameters simultaneously. The principle parameter is the wind power generation, and the other parameter depends on the different types of loads. The types of loads are ZIP, exponential recovery, dynamic induction loads, and composite load models. To study the effects of the induction motor loads, the proportion of the static component in the motor load is changed and assessed with respect to their mechanical loads. Wind generation margin boundaries are traced, and saddle‐node, Hopf, and limit‐induced bifurcation branches are obtained, delimiting the stable and unstable operating regions in the parameter space. The analysis presented in this paper can pave the way for determining methods for improving and monitoring these margins with consideration to the system parameters and load composition.

Generalised approach to modelling a three-tiered microbial food-web

The complexity of the anaerobic digestion process has motivated the development of complex models, such as the widely used Anaerobic Digestion Model No. 1. However, this complexity makes it intractable to identify the stability profile coupled to the asymptotic behaviour of existing steady-states as a function of conventional chemostat operating parameters (substrate inflow concentration and dilution rate). In a previous study this model was simplified and reduced to its very backbone to describe a three-tiered chlorophenol mineralising food-web, with its stability analysed numerically using consensus values for the various biological parameters of the Monod growth functions. Steady-states where all organisms exist were always stable and non-oscillatory. Here we investigate a generalised form of this three-tiered food-web, whose kinetics do not rely on the specific kinetics of Monod form. The results are valid for a large class of growth kinetics as long as they keep the signs of their derivatives. We examine the existence and stability of the identified steady-states and find that, without a maintenance term, the stability of the system may be characterised analytically. These findings permit a better understanding of the operating region of the bifurcation diagram where all organisms exist, and its dependence on the biological parameters of the model. For the previously studied Monod kinetics, we identify four interesting cases that show this dependence of the operating diagram with respect to the biological parameters. When maintenance is included, it is necessary to perform numerical analysis. In both cases we verify the discovery of two important phenomena; i) the washout steady-state is always stable, and ii) a switch in dominance between two organisms competing for hydrogen results in the system becoming unstable and a loss in viability. We show that our approach results in the discovery of an unstable operating region in its positive steady-state, where all three organisms exist, a fact that has not been reported in a previous numerical study. This type of analysis can be used to determine critical behaviour in microbial communities in response to changing operating conditions.

A new self-propelled magnetic bearing with helical windings

In this work, a design is proposed for an active, permanent magnet based, self-propelled magnetic bearing, i.e. levitating motor having the following features: (i) simple winding structure, (ii) high load supporting capacity, (iii) no eccentricity sensors, (iv) stable confinement in all translational dimensions, (v) stable confinement in all rotational dimensions, and (vi) high efficiency. This design uses an architecture consisting of a helically wound three-phase stator, and a rotor with the magnets also arranged in a helical manner. Active control is used to excite the rotor at a torque angle lying in the second quadrant. This torque angle is independent of the rotor's position inside the stator cavity; hence the control algorithm is similar to that of a conventional permanent magnet synchronous motor. It is motivated through a physical argument that the bearing rotor develops a lift force proportional to the output torque and that it remains stably confined in space. These assertions are then proved rigorously through a calculation of the magnetic fields, forces and torques. The stiffness matrix of the system is presented and a discussion of stable and unstable operating regions is given.

Inherent operational characteristics and operational stability of a variable speed direct expansion air conditioning system

Previous studies on the inherent operational characteristics of a variable speed (VS) direct expansion (DX) air conditioning (A/C) system at a fixed degree of refrigerant superheat (DS) setting without considering its operational stability have been conducted. Therefore, a follow-up study on the inherent operational characteristics of a VS DX A/C system considering its operational stability has been carried out and the study results are reported. Using an experimental VS DX A/C system, the inherent correlations between its output total cooling capacity (TCC) and equipment sensible heat ratio (E SHR) at different combinations of compressor speed and supply fan speed were studied and the unstable operating points of speed combinations under different DS settings and inlet air states identified. The experimental results suggested while different DS settings may not significantly influence the inherent correlations between TCC and E SHR, but did impact the operational stability. A lower DS setting would result in a larger unstable operating region. Furthermore, VS operation and different inlet air states to the DX evaporator also influenced the operational stability. A higher compressor speed or a lower supply fan speed, and a lower inlet air temperature or relative humidity would lead to a higher chance to instability.

Unsteady numerical analysis of the rotating stall in pump- turbine geometry

Main challenges in energy sector nowadays are storing and recovering of a large amount of energy in a short time. Pumped Storage Power Plants (PSP), using reversible pump- turbines are among the most cost-efficient solution to answer these needs. To provide a rapid adjustment to the electrical grid, pump-turbines are subjects of quick switching between pumping and generating modes and to extended operation under off-design conditions. To maintain the stability of the grid, the continuous operating area of reversible pump-turbines must be free of hydraulic instabilities. One of the main sources of pumping mode instabilities is the presence of the rotating stall that occurs at the part load. It can be observed as periodic occurrence and decay of recirculation zones in the distributor regions. Consequently, the machine can be exposed to uncontrollable shift between the operating points with the significant discharge modification and the drop of the efficiency. The phenomenon is very complex, three-dimensional and demanding for the investigation. The paper presents cost- efficient numerical methodology that enables the accurate prediction and analysis of the rotating stall. The investigations were made on a reduced-scaled high head pump-turbine design. Unsteady numerical calculations were performed using code FINE/TurboTM and URANS equations. Local flow study was done to describe in details the governing mechanisms of the rotating stall. The analyses enable the investigations of the rotating stall frequencies, the number of stalled cells and the intensity of the rotating stall. Moreover, the unsteady calculations give very good prediction of the pump-turbine performance for both, stable and unstable operating regions. Numerical results show very good qualitative and quantitative agreement with the available experimental data.

On Active Surge Control of Compression Systems via Characteristic Linearization and Model Nonlinearity Cancellation

A simple approach of active surge control of compression systems is presented. Specifically, nonlinear components of the pressure ratio and rotating speed states of the Moore-Greitzer model are transferred into the input vectors. Subsequently, the compressor characteristic is linearized into two modes, which describe the stable region and the unstable region respectively. As a result, the system’s state and input matrices both appear linear, to which linear realization and analysis are applicable. A linear quadratic regulator plus integrator is then chosen as closed-loop controller. By simulation it was shown that the modified model and characteristics can describe surge behavior, while the closed-loop controller can stabilize the system in the unstable operating region. The last-mentioned was achieved when massflow was 5.38 per cent less than the surge point.

Robust Active LED Driver with High Power Factor and Low Total Harmonic Distortion Compatible with a Rapid-Start Ballast

A new active LED driver with high power factor (PF) and low total harmonic distortion (THD) compatible with a rapid-start ballast is proposed. An LC input filter is attached to the ballast to increase PF and reduce THD. A boost converter is then installed to regulate the LED current, where an unstable operating region has been newly identified. The unstable region is successfully stabilized by feedback control with two zeroes. The extremely high overall system of the 10th order is completely analyzed by the newly introduced phasor transformed circuits in static and dynamic analyses. Although a small DC capacitor is utilized, the flicker percentage of the LED is drastically mitigated to 1% by the fast controller. The proposed LED driver that employs a simple controller with a start-up circuit is verified by extensive experiments whose results are in good agreement with the design.

Influence of Dihedral Stacking on The Performance of An Axial Fan

This paper presents the effect of positive dihedral (lean) on the aerodynamic performance of a low speed axial fan. The blade profiles of the reference (base) fan are stacked on a radial line at the centre of gravity of each profile. The stacking line of the fan with the dihedral, along which the blade profiles are shifted in the direction perpendicular to the chordline, makes an angle of 45 in the radial direction. The performances of the both fans are investigated by means of ANSYS CFX commercial CFD software and are validated by experiments. Both of the computational and the experimental results show that positive dihedral removes the unstable operation region of the fan. Moreover, the total pressure rise and the total-to-total efficiency are increased at low flowrates. The detailed investigation shows that the induced radial velocity in the outward direction may be the reason of the positive effect of the dihedral at low flowrates. As a result, dihedral stacking extends the stable working range of the fan by removing the unstable region.

Enhanced stability of dispersion-managed mode-locked fiber lasers with near-zero net cavity dispersion by high-contrast saturable absorbers

We experimentally investigate the stability of dispersion-managed mode-locked fiber lasers using carbon-nanotube-based saturable absorbers (SAs) with different modulation depths. An unstable operation region of the mode-locked fiber laser with near-zero net cavity dispersion is observed, where the laser produces random pulse burst rather than stable pulse train. Through the implementation of high-contrast SAs in the laser, the unstable region is found to be shrunk by ~31.3% when the modulation depth of the SAs increases from 6.4% to 12.5%. The numerical simulation is consistent with the experimental observation.

Experimental analysis on the performance of a turbocharger compressor in the unstable operating region and close to the surge limit

To make simulation models able to accurately predict engine performance, a better understanding of compressor behavior over an extended range can be accomplished by using a specialized test facility and measuring equipment. Besides, the correct surge line position is another important aspect to be considered to optimize engine-turbocharger matching calculation. In the paper the results of an experimental investigation developed on a turbocharger compressor for heavy duty vehicle application is presented. The study was focused on the definition of surge line position adopting different methods and on the evaluation of compressor performance over an extended range, taking into account compressor behavior both in the stable and unstable operating region.

Multivalued Stability Map of an Injection-Locked Semiconductor Laser

We present a novel and detailed analysis of the locking range and the stability map for side-mode injection-locked in-plane semiconductor multimode lasers. By including the usually neglected unlocked modes in our model, we predict a multivalued locking range and stability map for this type of lasers. We also explain and relate, the previously noticed slave laser bistability phenomenon with the multivalued character of the locking range and stability map, and experimentally validate our findings. Moreover, we find that the unstable operating region, commonly found in literature by stability analysis of the injection-locked mode alone, is actually much smaller.

Research on the unstable operating region of axial-flow and mixed flow pump

The unstable operating region affected safety of pump start-up and limited the range of stable operating. When there are three flowrates points matching along with one lift, the hydraulic unstable operating region happened. The range region of unstable operation region is from peak to bottom of performance curve when the axial flow pump was test on the closed test rig. There are two factors, rotating stall and bad inlet condition, which cause the unstable operating region. The unstable operating regions of different pumping system are presented. The unsteady CFD calculations were done to present the internal flow pattern and hydraulic pressure when axial flow pump and mixed flow pump were operated on the unstable operating region. The frequency spectrum is given of one of the force components in radial direction, as measured in the whriling frame of reference. It is important to prevent and avoid unstable operating region along with the construction of South to North water transfer of China and reconstruction of large scale pumping station.

Dynamic behavior analysis of carboxymethylcellulose hydrolysis in a chemostat

At the present time cellulosic waste substrates is a subject of global relevance because is an alternative source for biofuel production, the complex nature of this substrate and the presence of microorganisms for its biodegradation may result in complex dynamics which are important to understand why in many cases could have negative effects in the productivity process. In this paper dynamical behavior analysis of a chemostat model was carried out for two unstructured kinetic growth models (Luong and Han-Levenspiel), choosing as study case the carboxymethylcellulose hydrolysis by Cellulomonas cellulans, where differences related with multiplicity of steady states, hysteresis, periodicity and unstable operating regions were pointed out.

Nonlinear MPC of a multi-zone multi-feed LDPE autoclave reactor

This paper discusses the design of a model-based multivariable nonlinear model predictive control (NMPC) formulation for the control of a multi-zone multi-feed LDPE autoclave reactor. Unscented Kalman filtering (UKF) state estimation was employed for online estimation of the plant states and disturbances. In addition to structural plant-model mismatch and noisy process measurements, the closed-loop performance of the UKF based NMPC scheme was investigated under parametric uncertainty in the kinetic rate constants. The closed-loop NMPC performance was also assessed for polymer grade changes, and for disturbance rejection at both open-loop stable and unstable operating regions.

다단 천음속 압축기의 유동 불안정성에 관한 실험적 연구

This study presents unsteady and unstable characteristics of three stage transonic axial compressor, developed by Korea Aerospace Research Institute. As approaching to the unstable operating region at the 103% design speed of the compressor, a modal type stall precursor appears in front of highly loaded 3rd rotor row at first, and it propagates to the upstream. On the contrary, actual stall cell initiates from the stall precursor in front of the 1st rotor row, and it propagates to the downstream of the compressor. After the stall region reached the 3rd stage and stall cell rotates circumferentially about 360 deg, it develops to one dimensional compressor surge mode. It shows a mild surge behaviour with 3∼4 Hz frequency. From the test data, it can be suggested that there is a priority to give an optimum blade loading distributions to construct a multi stage transonic axial compressor stages either to secure more stable compressor operating ranges, or to maximize the compressor efficiency.