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The energy structure change of more electric aircraft makes the aircraft airborne system more complicated. Each subsystem realizes the transmission, interaction, and conversion of energy and information through the dynamic coupling and coordinated control of electrical energy, mechanical energy, hydraulic energy, and thermal energy. This paper applies the multiphysical domain modeling method with the parameter identification according to the original model data. Based on the power conversion relationship of electrical equipment, it defines the port with the power potential variable and flow variable and is supplemented by the information control. It can show the dynamic characteristics, power conversion, and loss characteristics of the device itself. The models can conveniently perform the large-scale system integration, which not only can build the complex electrical equipment formed by multiphysical domain models with the series connection but also can build a complex power supply system formed by multiphysical domain models with the parallel connection.

The secondary energy of the more electric aircraft gradually uses electrical energy to replace hydraulic energy and pneumatic energy for the aircraft energy optimization [

The electrical equipment operation of the more electric aircraft involves the transmission, interaction, and conversion of the multiphysical domain, such as electrical energy, mechanical energy, hydraulic energy, thermal energy, and information [

In order to realize the simulation of the electrical system multiphysical domain power conversion, the digital model of the electrical equipment is required to be established. The multiphysical domain modeling can solve the coupling problems [

The equivalent circuit modeling has the disadvantage because the structure is simplified. The more details and nonlinear characteristics cannot be accurately represented. The modeling workload by the analysis structural modeling is relatively large, and the nonlinear modeling is especially cumbersome. The input and output may be variables of different physical domains. When the electrical system integration is achieved, the system structure may be confused and inconvenient in engineering application.

The bond graph method is applied for the hydraulic system [

This paper applies the multiphysical domain modeling method with the parameter identification according to the original model data. The analytical model based on the energy conversion process of the electrical equipment is supplemented by the information control. The model uses the energy transmission between the electrical equipment as the interface between the models, enabling the large-scale integrated electrical system simulation, and the simulation operation speed is improved.

Compared with the traditional aircraft, the increase in electrical equipment of more electric aircraft is the electrical drive equipment. The electromechanical actuator (EMA) [

The electromechanical actuator is taken as an example to analyze the structural characteristics of the electrical equipment. The EMA is an electrical drive position servo control system for the aircraft surface. The physical model of the EMA is shown in Figure

Principle block diagram of the electromechanical actuator.

The electrical drive equipment shown in Figure

From the perspective of energy conversion, the electromechanical actuator performs the conversion of the electrical energy to mechanical energy, and the conversion power is determined by the fight mission. At the same time, all parts of the equipment have the power loss. It transforms parts of the electrical energy and mechanical energy into thermal energy and forms a secondary power conversion process.

The main function of the information conversion part is to complete the control during the equipment. For example, the EMA realizes the closed-loop control of the rudder surface position _{a}, the motor speed Ω_{m}, and the armature current _{d}. In addition, it can also monitor the running status of the device and communicate with the host computer and other devices.

The physical model shown in Figure

According to the structure of the electrical device shown in Figure

Model structure of the electrical equipment.

The PCM represents the device power conversion process. The power conversion is mainly the conversion between two kinds of energy sources. The thermal energy generated by the power loss is the third additional energy conversion relationship for the performance analysis of the power loss and efficiency.

The SCM function of the electrical equipment is the same as that of the information conversion part in Figure

The PCM shown in Figure

When the power conversion model shown in Figure

Potential variables and flow variables for different power types.

Power form | Potential variable | Flow variable |

Electrical power | Voltage | Current |

Rotating machine power | Speed Ω (rad/s) | Torque |

Linear machine power | Force | Moving speed |

Hydraulic power | Pressure | Flow ^{3}/s) |

Thermal power | Temperature | Flow (heat flow) Φ (W) |

Electrical power | Voltage | Current |

The PCM of the electrical equipment model can be represented as Figure _{s}, and the flow variable is represented as _{s}. The potential variable of the output power (load power) is _{L}, and the flow variable is _{L}. The power loss output is generally thermal power. The ambient temperature

Input/output variables of the power transformation model. (a) Variable relationship of electrical equipment PCM. (b) Variable relationship of electromechanical actuator PCM.

According to the relationship of the PCM input/output variables shown in Figure _{1} (_{2} (_{3} (_{4} (

For the electromechanical actuator shown in Figure

The potential variable of the input power in equation (_{s}, and the flow variable is the supply current _{s}. The potential variable of the output power is the angular velocity Ω_{a} of the aircraft rudder surface, and the flow variable is the resistance torque _{L} of the rudder surface.

The energy conversion relationship of the entire device is shown in equation (_{sc} and _{Lc} are the device control and interference variables, respectively, which are generated by the SCM and have a certain functional relationship with _{s} and _{L}. _{1} (_{2} (_{3} (_{4} (

The electromechanical actuator shown in Figure _{sc}, and the relationship with the power source voltage _{s} is _{sc} = DU_{s}. _{Lc} is the load torque corresponding to the electromagnetic torque. In addition to the resistance torque _{L} on the rudder surface, it will also include the friction torque and damping torque on the motor and reducer.

The power loss model of equation (_{s} and the output power _{L} can also be approximated and described as follows:

The electromechanical actuator shown in Figure _{ec}, the copper loss _{cu} of the motor, the iron loss _{fe} of the motor, the mechanical loss _{m} caused by the friction of the motor and the reducer, and the power loss of the electronic device which can be approximated to the motor copper loss _{cu} and classified into the copper loss. Therefore, the power loss can be described as_{d} is the armature current. Due to the motor moment inertia, the electrical drive device is expressed as the device containing the energy storage component. If equation (

The SCM of the multiphysical domain model is used to simulate the information conversion of the electrical equipment. It can realize the operation control and the state measurement of the system, such as the functions of the controller and the sensor in Figure

For the multiphysical domain model described in Figure _{sc}. The second function is to generate the disturbance signal _{Lc} according to the operating state. It can be described as

The electromechanical actuator shown in Figure _{a}, the motor speed Ω_{m}, and the motor armature current _{d}. The control voltage signal should be_{acr}, _{asr}, and _{apr} are the transfer functions of current, speed, and position regulator, _{d}_{m}_{a}_{θ} is the hinge moment coefficient of the rudder surface, which is _{L} = _{θ}_{a}. The load torque on the actuator is_{f} is the friction torque of the motor and the reducer and _{Ω} is the speed damping coefficient of the motor.

The function of the SCM operation state measurement is to simulate the sensor function of the electrical equipment. The test signal can be used as a feedback signal of the system control and provide to the monitoring device or the host computer, which is the output information in Figure

The SCM test information is defined as

For the EMA control and disturbance signals in equations (_{d} is the motor armature current, _{s} is the power supply current, _{s} is the proportional coefficient, Ω_{a} is the angular velocity of the aircraft rudder surface, Ω_{m} is the motor speed, _{i} is the reduction ratio of the reduction gear, and _{a} is the rudder surface position.

If it needs to know other signal information, such as the motor electromagnetic torque _{e}, it can be described by_{t} is the torque factor.

The electromechanical actuator is used as multiphysical domain modeling object, and the consistency is verified by comparison with the original model simulation results.

The multiphysical domain modeling object is the EMA model shown in Figure

The multiphysical domain modeling is mainly to establish the PCM transfer functions of _{1} (_{2} (_{3} (_{4} (_{1} (_{4} (

Since the EMA in Figure _{sc}, and it is simulated with _{L} = 0 to obtain the unloaded angular velocity Ω_{a0} of the rudder surface and the power supply current _{s0}. Then, the load torque _{L} is set to a step signal for simulation, and the speed signal _{a} and the power source current _{s} are obtained. The obtained signals are, respectively, identified and the PCM is described as follows:

Combining the power conversion module of equation (

The reference position _{a}_{a} (potential variable) and the power supply current _{s} (flow variable). The curves are shown in Figure

Simulation results of EMA models. (a) Actuator speed. (b) Power supply current. (c) Power loss.

It can be seen from Figure

Another advantage of the multiphysical domain model is that it facilitates large-scale integration to establish the complex electrical system. The multiphysical domain model integration is based on the energy conversion relationship, and there are two types of series integration and parallel integration.

The multiphysical domain model of complex electrical equipment can be obtained by the serial integration of multiple simple multiphysical domain models.

For example, the EHA consists of the motor, the hydraulic pump, and the hydraulic actuator. If the EHA original model is available, the same EMA signal identification modeling method as equation (

EHA model implemented by serial integration.

Since the EHA is controlled by the motor speed to realize the flow control of the hydraulic pump and the position control of the actuator, the control signal from the information conversion module is applied to the motor model. In addition, the EHA output is a linear motion; therefore, the potential variable of the output power according to Table _{a}, and the flow variable is the moving speed

For example, the main parameters of the EHA are the power supply voltage 270VDC, the motor rated speed 8000r/min, the actuator rated moving speed 0.12 m/s, and the maximum force 200 kN. The EHA model is simulated with the position which is set to 80 mm. The simulation waveforms are shown in Figure

Simulation waveforms of each EHA connection point. (a) Moving position, power, and variables of the rudder surface. (b) Hydraulic power and variables of the hydraulic pump. (c) Mechanical power and variables of the motor. (d) Electrical power and variables of the motor. (e) Power loss of EHA.

It can be seen from the simulation results that the EHA model obtained by the series integration of the multiphysical domain model can not only simulate the EHA input and output variables and power data but also observe the waveforms of each connection point in order to analyze the correctness of the model.

In the electrical system of the more electric aircraft, the power supply needs to provide electrical power for all the electrical equipment; that is, the electrical equipment forms the parallel structure on the bus bar. When all the electrical equipment is described by the multiphysical domain models, the structure is as shown in Figure

Parallel integration of the power supply system.

The output power of the power supply is the electrical energy. The potential variable is the power supply voltage _{s} connected to the potential variable _{si} of all electrical loads with the power supply side. The flow variable _{s} is the summation current of the electrical equipment input current, which is the power flow _{si} summation of all electrical loads.

The flight control system of the aircraft is taken as an example. The flight control system consists of the left and right ailerons, left and right elevators, and the rudder. It is assumed to be driven by the EMA, established with the power supply system shown in Figure

It is assumed that the aircraft continuously completes the climb phase, the combat phase (including the yaw, roll, and dive flight attitude), and the descent phase of the flight. The control signals are obtained by the flight control system models. The corresponding reference signal _{a}

Flight characteristics simulation of the flight control system. (a) Elevator power characteristics. (b) Aileron power characteristics. (c) Rudder power characteristics. (d) Output power characteristics of the power supply.

It can be seen from the simulation results shown in Figure

Since the electromechanical actuator belongs to the dynamic load of the short-time operation, the flight control system shows the pulse power of different sizes from the above figures. The power analysis for this type of system can only be done by the digital simulation.

The multiphysical domain model with the parameter identification according to the original model data is applied in this paper. It takes the power conversion process of the electrical equipment as the basic modeling and accurately expresses the power conversion and loss characteristics based on the dynamic characteristics of the device itself. The model based on the energy conversion relationship for system integration is to achieve the large-scale integration of the electrical system flexibly and the required digital simulation of the electrical system design.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.