Management strategy to mitigate voltage sags effects of a multi-motors system using ADALINE algorithm and cascade sliding mode control

ABSTRACT


INTRODUCTION
Many industrial applications require more than one motor.This is either because it is bulky in terms of volume (for example transport) or because the system necessitates distributed actuators (in the paper, textile and general web transport) [1], [2].These applications become multi-motors systems (MMS) [3], and multi-converters systems [4].Vehicle convoys (in the context of a smart highway with autonomous vehicles) and electric power transmission networks with generators and distributed loads are also included in this class of system [5].MMS on the other hand are extremely sensitive to power supply disruptions [6].Indeed, the most common disturbance problem is sudden voltage drops, also known as voltage sags [6].The IEEE 1159 standard defines them as a 0.1 to 0.9 pu.decrease in root mean square (RMS) voltage over a time period ranging from 0.5 cycles to 1 minute [7].Voltage-dips which are responsible for the majority of these disturbances, are primarily caused by the start-up of large driving loads and power system faults such as lightning.Because these faults can never be eliminated in the electrical system, we must design equipment that can withstand the most common voltage dips [8], [9].
A single motor failure in a MMS, or a brief loss of synchronism between motors, can jeopardize the entire process and necessitate a complete shutdown.Furthermore, shutting down motor loads due to voltage dips has several consequences.For example, a loss of synchronism with the flux causes re-acceleration with high inrush currents, a low power factor, and a very long fault clearance time, causing the voltage dip to be prolonged.As a result, a reset procedure is required [10].To reduce production losses and in some cases, limit the high currents required to restart motors after a voltage dip, equipment and strategies to keep the drives running during short and long voltage dips have been developed.The solutions are diverse, as are the costs: Changes to the protection logic to avoid premature shutdown, the use of backup power sources, changes to the power converter structure [10], [11], and use the rotating machines kinetic energy to maintain synchronism with the machine's flux to allow for efficient re-acceleration [12].
The main goal of this work is to develop a voltage sag management strategy for a MMS consisting of two AC drives with a common DC bus that are mechanically coupled by web with an adjustable tension.Furthermore, this work aims to contribute to the development of control methods that maintain the synchronism between the drives in the presence of voltage dips.The proposed management strategy is based on the principle of recovering the system's kinetic energy and the converter's current reversibility.This proposal makes no significant changes to the traditional structure of MMS with common DC bus and can be implemented using sliding mode controllers.
This paper is organized as follows: i) The nonlinear model of a simple winder system driven by two three-phase induction motors is presented in section 2; ii) The voltage-sag management strategy consists of three parts, presented in section 3. The adaptive linear neuron or later adaptive linear element (ADALINE) method, which generate the three-phase voltage-sag alarm signal quickly, the changes to M2 machine's operation mode based on logical conditions, and the modification of the control topology; iii) Simulation is carried out in section 4 to validate the relevance of the proposed solution; and iv) Finally, section 5 concludes the paper.

MATHEMATICAL MODELS OF THE WEB WINDING SYSTEM
A winding system, a good illustration of MMS, is composed of at least two rolls, mechanically coupled by a band of elastic material and driven by two motors.In a simple case, one motor winds the material at a given velocity while the other one serves to maintain a constant mechanical tension  2 of the material as it is wound Figure 1 [3].

Mechanical models
Web-transport systems model is based on three laws, which enable to calculate the web tension between two rolls [13]: -Hooke's law: To model the material's elasticity, the tension T is a function of its relative elongation  and mechanical properties (Young's modulus and band section)  = ...-Coulomb's law: It expresses the variation in tension between the material and the roller in the contact zone.
-Mass conservation law: That shows the coupling between web velocity and web tension.These laws allow the calculation of web tension between two rolls.The mechanical tension  2 of the material between the rolls can be characterized as a function of the web length L and the linear speeds of the roller  1 and  2 .Where  1 the input tension, E the Young modulus of the band and S the band section.

Electric drives models
Three-phase squirrel-cage induction machines are the most commonly used machines for converting electrical energy into mechanical energy.They can function both as motor and as generator.These machines are frequently used in high-power applications in the field of adjustable-speed drives.
A model based on the equivalent-circuit equations of the motor is generally sufficient to synthesize the control laws.Electrical dynamic model of three-phase Y-connected induction motor   can be expressed in the d-q synchronously rotating frame as (2) [5], where (  ,   ) are the stator voltages and (  ,   ) are the stator currents in (d, q) coordinates.  is the direct component of the rotor flux (the quadrature component of the rotor flux is equal to zero, i.e.,   = 0, due to indirect rotor field-oriented control (IRFOC).Thus, the electromagnetic torque is given by (3).

Behavior of the DC bus in voltage-sags mode
Bidirectional DC/AC converters are used to control three-phase machines, especially in MMS with a common DC bus.They offer the possibility to transfer power either, from the common DC bus to the machines or from the machines to the DC bus.Theoretically, Figure 2 shows a constant power flow between the machines is possible due to the reversibility of the converter [14].
During power interrupt or in rectifier blocked condition, the DC link voltage (  ) is directly affected by the operating mode of the machine.Consequently, when the machine operates in motor mode,   decreases, and when the machine operates in generator mode,   is increased.The rate of change,   /, is related to the capacity of the DC link, to the power of the machine, to the combined converter-machine efficiency and to the value of   .  =     is the electromagnetic power, with   the electromagnetic Under the same condition, the dc-link voltage variation   / is a function of induction motors electromagnetic powers and the inverters efficiency.It will be enough to manage the power of the machines so that one of them can operate in motor mode when the other is working in generator mode, in order to maintain the electrical voltage of the DC-link constant.DC-link voltage regulation is possible in steady state if power relation ( 5) is satisfied.It has a single neuron with a linear activation function and an input in the form of a vector x(k).It was proposed and developed by Widrow [15].The structure and algorithm of the ADALINE network is described in Figure 4 [7].ADALINE has been successfully used to estimate the amplitude and phase of a signal's fundamentals.

Control structure
The control structure shown in Figure 3, is implemented using sliding mode control speed controllers, indirect rotor field-oriented controllers (IRFOC) and another sliding mode control controller is used for the web mechanical tension control with external web tension set point   .This controller generates the speed set point for M1 in a cascade-control loop structure.A speed sliding mode controller (SSMC) is designed to control the speed of an induction motor fed by three phase voltage source inverters controlled by pulse width modulation (PWM) technique [16], [17].
In this work, the sliding mode control scheme is illustrated in Figure 5. Sliding mode controller is a nonlinear controller based on the principles of variable structure control.Similar to DC motors, speed control of induction motors can be realized in a cascaded control scheme [18], with a current controller in the inner loop and a speed controller in the outer loop.In general, the mechanical equation of an induction motor can be written as providing the reference currents    and    for the inner loop [19].the sliding mode and in permanent regime,  ̇ = 0 ,   = 0 and  _  = 0 , the equivalent control can be given as (6).

Rotor speed controller
During the convergence mode, the condition  ̇   < 0 should be verified and the discontinue control can be expressed as (7).

Rotor flux controller
The flux surface is chosen as follows:   =    −   and the derivative of the surface is given by:  ̇ = ̇  − ̇.During the sliding mode and in permanent regime,  ̇ = 0 ,   = 0 and  _  = 0, the equivalent control can be given as (9).
During the convergence mode, the condition  ̇   < 0 should be verified and the discontinue control can be expressed as (10).
Finally, the direct current reference is given by (11).
=   Sgn(   ) + For the indirect rotor field-oriented control (IRFOC) tuning parameters we need two surfaces    =    −   and    =    −   the first for the   regulator and the second for   regulator.Deriving of the two surfaces and considering the equations of the system (2), we find in (12).During the sliding mode,    = 0,    = 0,  ̇ = 0,  ̇ = 0,  _  = 0,   _  = 0 and the equivalent control actions are done as (13).
During the convergence mode, the conditions  ̇    < 0 and  ̇    < 0 must be verified and the discontinue control actions are given as (14).
Finally, the two regulators control laws, are given by (15).
The product of the surface and its derivative must be less than or equal to zero for the system to be stable.To ensure this condition, the parameters   ,    ,  i  and  i  should first be taken positive and then adjusted to the appropriate values which correspond to the highest performances of the system.These parameters have been chosen in order to: ensure quick convergence, impose sliding dynamics and convergence, and limit current to a value that allows for maximum torque [20], [21].
Now check this condition by evaluating    ̇ and select    as (16).
We find the conditions for the existence of the sliding mode for surfaces    ,    , and    using the same method.

Voltage-sag mitigation strategy
The voltage-sag management method consists of two parts: a change in M2 machine's operation mode depending on logical conditions and a change in the control topology.M1 and M2 machines have only one working mode in a typical system and under standard voltage conditions, namely the « motor mode ».Four modes of operation are considered in this proposal, each of which is dependent on grid voltage, DC bus voltage, and process speed.« Motor mode », « Free mode », « Vdc control », and « Stopping mode » are the four options available Figure 5, where: -Motor mode: M2 machine SMC controller acts as a speed controller, with an external set-point ω 2ref , and the speed of the M1 machine is always controlled by the mechanical tension controller, which generates a set-point -Free mode: M2 machine SMC controller acts as a speed controller, with speed set-point equal to the motor speed (ω 2ref = ω).-Vdc control: M2 machine controller's speed set-point is replaced by a voltage set-point, the controller gains are changed to allow DC bus voltage control, and M2 machine changes to generator mode as necessary.The system shifts to "free mode" if a rise in DC bus voltage is observed and the voltage dip persists.The system changes to "Stopped" mode if the system speed is reduced below the minimum speed (  ) and the grid voltage is not restored.This mode enforces a controlled braking of the system.The objective of the control in this case is to keep the rectifier output voltage constant, regardless of the speed and load over a wide range of variation.Furthermore, from the desired value of the DC voltage, it is possible to express the reference power by: Neglecting the losses, the torque expression can be written as in (19): According to electromagnetic torque (3), the latter can be controlled by the quadrature stator current component   [24], [25].-Stopping mode: SSMC controller for M2 machine in stopping mode works as a speed controller with a zero-speed set-point ( 2 = 0)

SIMULATION RESULTS
A first evaluation of the relevance of the proposed voltage-dip detection algorithm and management strategy is performed by simulation.The described algorithms and the models of the MMS have been implemented in MATLAB/Simulink/SimPowerSystems in order to perform simulations under different conditions.For voltage-sags detection, three distinct estimators are implemented in the "ADALINE sags detection algorithm" block shown in Figure 6.These are S-Functions written in C language.An S-Function is a Simulink block description language that can be written either in MATLAB language, C, C++, and Ada or Fortran.An S-function allows creating new Simulink blocks by the user.This program is then compiled using the "mex" command.

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"SAG mitigation strategy" block presented in Figure 7, is implemented using Stateflow.This is a state diagram or state-transition scheme consisting of a graphical representation of the finite number of states in a state machine, the state transitions, and the rules that control these.We considered that Ml and M2 machines rotate at different speeds and that they have different moments of inertia.This is the typical case in a material winding system.Mechanical characteristics used in simulation work are listed in Table 1.
Figures 8-15 depict the system's response to a voltage-sag with a depth of 50% and a duration equal to the   produced when the system operates at a speed of 70 rad/s.Note that t = 4s represents the start time of the voltage-dip.Furthermore, the difference in speed between roller 1 and roller 2 is negligible.Electromagnetic torques Figure 13 show significant differences, owing to the moments of inertia involved.Trajectories of DC bus voltage as shown in Figure 11, the roller speed is shown in Figure 12 and mechanical tension shown in Figure 14 show that mechanical tension and DC bus voltage can be controlled even if the machines reduce their speed by less than 20%.

CONCLUSION
This paper proposed voltage-dip management strategy for a MMS consisting of two asynchronous machines mechanically coupled by an elastic material and connected to a common DC bus.A control system based on the sliding mode was designed, and the stability of the control law was proven.Simulation was used to test the functionality and the relevance of this strategy, and obtained results demonstrated that during the voltage-sag, DC bus voltage was effectively controlled.The significance of rapid detection of the voltage-dip by ADALINE method and the quick correct change of the machine's operation mode has been emphasized.This strategy is based on the measurement of the DC bus voltage to allow its control and to maintain process continuity.Simulation results also showed the efficiency of the proposed strategy to manage the voltage-dip in the coupled MMS, demonstrating that they can operate properly before, during, and after the voltage-dip.However, the system's autonomous operation is limited by the efficiency of the system's total inertia and the operating speed when voltage-dip occurs.The machine's kinetic energy at the start of the voltage dip is a function of the square of the speed at the start of the voltage dip and the inertia.the regulation operating time, determined by the machine's energy at the start of the voltage dip and the power absorbed by the load on the DC bus, corresponds to the case of perfect recovery of the machine's kinetic energy.On the one hand, the goal of future research is to set up an experimental test bench to emulate a mechanically coupled industrial multi-motor system.And secondly, the implementation of a proposed voltage dip management strategy for a mechanically coupled multi-motor system using DSP boards and dSPACE rapid prototyping systems.

Figure 2 .
Figure 2. Equivalent circuit of two machines connected to a common DC bus

Figure 6 .
Figure 6.State diagram showing the four operating modes of the voltage-dip management strategy: motor mode, free mode, Vdc control, and stopping mode

Figure 7 .
Figure 7. Simulink model of detection algorithm and management strategy

Table 1
explains the parameters of the MMS.

Table 1 .
Rating parameters of the MMS