Variable DC Bus Voltage Control Scheme for the More Electric Aircraft Power Generation System

This paper aims to introduce a control scheme that offers variable voltage control for more electric aircraft electrical power systems. This control scheme allows increased power intake to the loads by variation of the bus voltage in addition to other key control functions for a generator system. The load considered is the electro-thermal based icing protection system that allows variation in operational voltage. The controllers are designed based on their respective derived plants for the main requirement of stable operation. The control scheme is tested in simulation to demonstrate the variable voltage concept along with the other operational capabilities.


I. INTRODUCTION
The more electric aircraft (MEA) trend has been gaining traction through enabling technologies from power electronics and electrical machines. This type of aircraft aims to increase the reliance on electrical power on-board aircraft for load applications that have been traditionally been powered by pneumatic, hydraulic, or mechanical power. Such configuration may offer benefits in terms of design, prognostics, and efficiency [1,2].
One of the aircraft loads is the icing protection systems, where various methods can be employed to prevent/remove ice on the flight surfaces. This can be done via mechanical boots, anti-freeze chemicals, bleed air from the aircraft engines, or heat from resistive elements (electro-thermal solution) [3,4] where the latter would be in line with the MEA initiative. The use of resistive elements help save weight when compared to the current bleed air system as it reduces the need of heavy and inflexible pipes [3]. The reduced reliance on bleed air allows the engine to be more aerodynamically efficient [5]. Another advantage of using this method is that it does not pollute the environment or damage the wing structure.
The use of electro-thermal icing protection system (eIPS) requires large amounts of power in comparison to bleed air based systems. The B787 de-icing power consumption was reported to be between 45 to 75kW. If the system is set to antiice mode, the power demand increases drastically up to 200kW [4,6]. This may limit the capability of the eIPS to be utilised on small surface areas of the aircraft depending on generator power availability. Dedicated electrical generators may be necessary to meet the eIPS power requirements [7].
As such, the electrical power generation system would have to undergo significant changes in the categories of power output density, power rating, and reliability to supply the increase in load demand [4]. The core modification is the exclusion of constant frequency gearbox commonly used in civil aircraft which thereby allows direct interface engine connection to the electrical generator. The variable frequency electrical power generated can then be regulated using power electronic converters.
One possible configuration between the generator system and the eIPS is interface connection via the main buses and have local converters/controllers to regulate the load power consumed. While this method is applicable, the amount of power may be limited by the constant bus voltage and current limit rating of the power converter. Another method is to establish a dedicated bus for the eIPS as seen in Fig. 1. This will ensure that other sensitive loads are not affected by the variable voltage levels. The bus voltage does not need to be fixed on the eIPS bus as the eIPS consists of mainly resistive loads. When the eIPS demands for very high power (i.e., anti-icing), then above rated voltage levels can be set and this is the variable voltage concept. An advantage of this topology is that it eliminates the need for local controllers which indirectly reduces the overall aircraft weight. This paper introduces a control scheme that enables the variable voltage concept. The content is structured as follows; the power system is detailed in Section II and the proposed accompanying control scheme is described in Section III. Analysis and the design of the controllers are explained in Section IV, with the results and conclusions in Section V and VI respectively. converter can be connected to the main DC bus that feeds the various electrical loads or to a dedicated eIPS bus via a contactor. The eIPS can be represented as a purely resistive loads as its primary function is to generate heat for icing protection purposes. On the main bus are all other loads such as the environmental conditioning systems and cabin electrical equipment. While these loads are cut off when the eIPS is powered by the generator, it is assumed that the loads which are essential are powered by another source such as battery systems or auxiliary power unit. For this study, the power system is connected to the eIPS bus to enable the demonstration of the control scheme's full functionalities. The high level control that determines the bus connection is not considered in this paper. The AC components of the power system are deduced in rotational reference dq frame [8]. Hence, the following are the main equation for the investigated power system:

II. ELECTRICAL POWER SYSTEM
vd,q and id,q are the PMM stator voltages and currents, Ld,q are the PMM stator inductances, Rs is the stator resistance, ωe is the electrical speed, and ψm is the machine flux. Edc and idc are the bus voltages and currents, C is the bus capacitance, and Rw is the resistance of eIPS load.

III. CONTROL SCHEME
There are various functions that should be undertaken by the power system. The main tasks is bus voltage regulation (typically 270V for high voltage DC buses) to ensure that the electrical loads can operate nominally. The other task is to ensure that the current does not exceed the converter ratings limit. Flux weakening may be considered to maintain converter controllability when operating in high speed regions (up to 32,000rpm) [9]. Literature covering the controller design for the MEA generator systems has been covered in [9] and [10]. The control schemes in the literature were designed to accomplish the functionalities stated earlier, however another control scheme has to be considered for the variable voltage concept. In addition to the previous functionalities, the new control scheme has to regulate the power of the eWIPS load that will vary the bus voltage levels.
In principle, the variation of bus voltage levels changes the amount of power supplied to the eIPS via the equation: where P is the power required by the eIPS, V is the bus voltage, and R is the eIPS total resistance. The concept is that if R is kept constant, then P can be increased if V increases. Fig. 2 and Fig. 3 shows the proposed inner and outer control loops respectively. mabc and mdq are the modulation index in three phase and dq frame respectively. mlim is the maximum modulation index and mdlim is the limit imposed on md. ismax and is are the stator current and its limit. Pdc is the DC power and ks depends on the modulation scheme to be used for the power converter [11]. Variables with the superscript * denotes the reference values. The numbered iq * are corresponding to the outer loop controllers output.
The inner loops have two current controllers for the dq currents, Wid and Wiq. Feedforward compensation are also added to the outputs of the controllers and they are scaled to modulation indexes by Edcks. A dynamic limit is used to employ flux weakening in this control scheme, whereby the modulation index should not exceed its limit following the equation: For this study, mlim is set to 1 for full use of the available voltage [11]. When the limit is reached, i.e., within flux weakening region, the q-axis control loop shall determine the value for md which then introduces id as the reactive current to de-flux the PMM. Outside the flux weakening region, Wid is set to control id to 0. Another dynamic limit is used to ensure that vq is within the limit when operating in flux weakening range: The outer control loop (Fig. 3) consists of three controllers to fulfil the functions of constant Edc, Pdc, and ismax. The Edc controller, We, can be used to regulate the bus voltage to a constant value. It can also be used with the eIPS bus if only nominal power is required. The Pdc controller, Wp, is designed to control the power sent to the eIPS bus. This controller is setup for uni-directional power flow to only send power to the bus. The last controller, Wis, is for is limitation purpose as there is a lack of current restrictions present within the control scheme. When is exceeds its reference value, iq2 * reduces in order to meet the following current limit: If is is less than ismax, then Wis output is constrained to zero to prevent control conflicts. All the controllers are considered to be PI type with anti-windup scheme and more details of their design will be explained in the following Section. The output of these controllers can be used to determine iq * . The three signals are compared using a minimum function and the smallest value at a given time is selected as iq * . In general, the magnitude of error of the controllers determine the controller priority. The minimum function is used as it is assumed that the power flow from the PMM to the bus is negative, hence iq is mainly negative. Back tracing is adapted in order to provide seamless transitions between the outer loop controllers [12]. This algorithm maintains all of the controllers' integrator states to be of similar value with respect to output iq * .

IV. ANALYSIS
The control plants are derived in this Section to help with the controller design. The analysis is performed in small signal domain which only considers linear plants. Non-linear equations such as (6) and (8) are linearised using Taylor's approximation around a given operating point. The parameters used can be seen in TABLE I. It is assumed that ωe is constant as the speed changes are much slower than the electrical components. The following are the small signal equations to be used to derive the outer control loop plants and their interactions can be shown in block diagram illustrated in Fig. 7.
Any variable with the o subscript denotes its initial operating point value. The inner current loop design has been discussed in details in [8] and the controller has been designed to achieve 500Hz bandwidth and 0.7 damping factor. The closed loop transfer function for iq is: where kpq and kiq are the proportional and integral terms of Wiq.

A. Edc control loop
The plant for this control loop should relate input Δiq * to ΔEdc. Using equation (13), each small signal term can be replaced with the other linear equations so that the plant can be found as:  The coefficients for a1e, a2e, a3e, b1e, b2e, and b3e are located in the Appendix section. This linear plant is verified with an equivalent non-linear model built in Simulink via step response comparison. Hence, the derived transfer function can be used to represent the plant for Edc.
The bode plot at different loads were also plotted as depicted in Fig. 4. As the load power increases more than 10kW, there is a tendency for the phase angle to exceed -180º which may cause instability when the closed loop gain is within that region. At higher frequencies the plant stabilises back again. Therefore, the plant at full load should be considered for the control design of We to take into account the unstable region. The gain margin at each load variation was found to be similar at about 21.8dB at the -180º crossover point. As long as the controller gain is selected to be within the gain margin, stability is ensured. This gain margin (up to k =12.3) is verified via a non-linear model built in Simulink and the instability is recorded when the controller gain is changed in Fig. 5.

B. Pdc control loop
From (15), it can be seen that the Pdc plant will relate closely to the newly derived Edc plant. Combining (14), (15), and (19) yields: The derived transfer function was also verified with an equivalent non-linear model. Fig. 6 shows the closed loop bode plots at different loads with a pure integral controller. The phase margin for 40kW was observed to be more than 180º, which indicates non-minimum phased characteristics. This would mean that the controller will have a limited gain range that allows stable operation. The gain margin at the 180º crossover was found to be 29.5 dB, which can be used as a reference during the controller design for this power system. If a proportional term is added to Wp, the gain has to be very small due to the resolution of the control variable (power in the order of 10 4 ) to the output iq (within 10 2 ). Hence, the proportional term can be omitted in order to simplify the control design process for Wp.

C. is control loop
Since the stator current is the control variable for this loop, hence the plant can be derived from the linearised current limit equation (12). Using the equations (9) to (18), the is plant can be derived to be: Similar to the previous analysis, the bode plot for this plant has been illustrated in Fig. 8 at operating loads up to 40kW. The phase does exceed 180º which indicates non-minimum phase as well. The gain margin was found to be 19.5dB at the highest load point and Wis is selected such that its gains are within the margin.
Based on the analysis in this Section, both Pdc and is plants have clear indication of non-minimum phase characteristics and their controllers should be designed carefully for stable operation. The selection of full load operating point for small signal analysis along with the linearised plants can help with the control design process. The following gains have been selected for the outer loop controllers to achieve reasonable bandwidth response within the stable margins and they are shown in

V. SIMULATION RESULTS
The time domain simulation results showing function of the proposed control scheme can be seen in Fig. 9 and Fig. 10. The operating points were selected such that the operation of each outer loop controllers are distinct. The simulation started with ωr = 20krpm, mlim = 1, Pdc * = 20kW, Rw = 25kW at 270V, and the ismax = 150A.
At t = 0.1s and 0.2s, there is incremental step increase of Pdc * = 3kW applied to demonstrate the function of Wp. During this period, it can be observed in the figures that Wp is online as its output, iq3 * , fulfils the minimum function and Pdc is controlled to the respective demand. As a result, Edc increases in order to satisfy the power demand, obeying equation (5). The power reduction can be observed at t = 0.7s and 0.8s respectively until Pdc * is lower than the nominal power consumed by Rw and We resumes control of Edc = 270V (t > 0.8s). The role of We is to maintain constant Edc if the other two controllers are not given priority.
At t = 0.3s, the speed was increased by 2krpm in order to increase is demand and to test the operation of Wis. This mainly increases the demand of id for flux weakening to maintain m = 1 as the speed goes higher. Eventually, is is limited to be within 150A and with an initial overshoot. The overshoot can be contained but can be difficult to be eliminated. Fortunately, this control scheme allows some level of current overshoot and throughout the operation, m has been kept at 1 using the modulation index limit.
The changes between the outer loop controllers can be observed through iq * . In Fig. 10, it can be seen that the controller output that demands the largest iq (in the negative direction) is selected for iq * . Moreover, slightly different transient dynamics can be seen in Edc, Pdc, and is between the changed and reverted operating points. This is due to the differences in their controller bandwidth response.

VI. CONCLUSION
The variable voltage concept has been studied for the MEA electrical power system with eIPS as its load. The control scheme can perform constant Edc control if connected to a main bus, Pdc control for power variation in the eIPS, is control for overall current limit, and flux weakening by restricting the Fig. 8. is plant with PI controller bode plot at different load levels.     Fig. 10. iq * , id, and ωr with respect to Fig. 9.