Research on optimal power flow of AC/DC hybrid system for civil more electric aircraft

Modern civil more electric aircraft often use AC/DC systems instead of AC systems to reduce the weight of the power system. Compared with the AC/DC system of the land power grid, the aircraft power system needs to pursue economic operation mode under more complex security constraints. This paper establishes the optimal power flow model of the AC/DC hybrid system of more electric aircraft, which takes minimizing the active power loss of the line as the optimization objective, including the steady-state operation constraints and security constraints of the AC/DC system. The interior point method and prediction correction interior point method are used to solve the model. Then, based on the simplified steady-state model of the B787 power system, the model and algorithm are verified by experiments. The experimental results show that by optimizing the power flow distribution of the power system, the power utilization efficiency of the system has been significantly improved, and its stability and reliability can also be better guaranteed.


Introduction
To cope with the operational pressure and challenges brought about by global warming and rising fuel prices, some countries have developed a new generation of civil more electric aircraft or all electric aircraft in order to reduce fuel consumption and pollution emissions recently.Therefore, more electric and all electric technology has increasingly become an important trend in the development of civil aircraft [1].In addition, the rapid development of variable-speed variable-frequency power systems and power electronics technology has helped the development of aircraft electrification [2].
The power system of the first generation of the civil more electric aircraft (MEA, such as A380 and B787) adopts AC-DC hybrid systems containing a large number of DC loads.However, the DC power grid without proper optimization not only has high active power loss but also reduces the voltage quality of AC nodes.At the same time, the aircraft power grid is an isolated microgrid, and its reliability determines the safety of the aircraft.The traditional method is to use redundant design to ensure reliability, but it will increase the weight of aircraft and fuel consumption.Therefore, how to capitalize on power generation resources and controllable devices to maximize the overall system operation efficiency under the premise of ensuring the reliability and safety of the aircraft electrical system has become one of the necessary challenges faced by the current MEA power system research [3].
Since the idea of optimal power flow (OPF) was put forward in the 1960s [4], OPF has become an indispensable network analysis and optimization tool for power system analysis and has greatly contributed to achieving the optimal allocation of resources, reducing the cost of power generation and transmission and improving the quality of service in the land power grid.Therefore, with the deepening of the electrification of MEA, it has become an inevitable trend to extend OPF to the power system of MEA.However, at present, the research on OPF of MEA power systems is relatively less.Most research focuses on the following aspects: fault-tolerant network architecture of power systems to reduce redundant wiring operation technology, load priority scheduling strategy, and model simulation research [5].These studies are mainly through the analysis of system stability, system architecture selection, power management, and load scheduling to achieve the purpose of reducing the weight of the power system and reducing system redundancy, but they do not involve the problem of OPF.
In [6], a load identification and control method was proposed to effectively manage the load system.In [7], the author solved the complexity of the DC load in the MEA and integrated it into a linear programming model.However, these studies did not consider the structural model of the converter in the power system and the transmission loss of the line.In [8], the author designed a power management system to control the efficient operation of the generator, considering the power loss in the system.However, the model is to study the simplified system and only considers the high voltage side voltage of the AC system.Research on power flow and optimal operation of AC/DC hybrid network for MEA is not sufficient.In [9], the solution method based on the OPF model was adopted, so as to reduce the transmission loss in the system and minimize the generator overload capacity.In the subsequent study [10], the author optimized the model and considered the power balance of high and low voltage bus and dc/dc converter to solve the most power routing problem in different flight stages.However, the voltage and current were not considered in the two studies, and only the active power flow of the DC grid was involved.
For the above problems, firstly we establish the mathematical model of the optimal power flow problem for the AC/DC hybrid system of more electric aircraft, considering its actual operation and control constraints.By solving the model, the optimal power flow distribution can be obtained, so as to realize the optimal dispatching and control of the power system.Then, to verify the feasibility of the established OPF model for MEA, this paper selects the B787 simplified power system structure as the experimental object and verifies the effectiveness of the established mathematical model by comparing the calculation results of the primal-dual interior point method (PDIPM) and Predictor-corrector primal-dual interior-point method (PCPDIPM).

Optimal Power Flow Mode
The main variable symbols used in this article are shown in Table 1.

Rectifier model and control mode
MEA is an independent microgrid with a hybrid AC/DC structure, as shown in Figure 1.Taking the B787 as an example, two generators produce 230 V/400 Hz AC power, which is converted through AC transformers and AC/DC converter units into 270 VDC, 28 VDC, and 115 V/400 Hz AC power.
The rectifier unit on the aircraft converts the AC voltage of the generator into a suitable DC voltage, which is generally realized by the transformer rectifier.A group of non-leading phase voltages and a group of leading 30 ° phase voltages are generated through a Y/Y/D phase-shifting transformer to form 12 pulses and become a double bridge rectifier [11].Its simplified structure is shown in Figure 2, where si si PQ * is the AC system power injected into the inverter transformer, di di PQ * is the DC system extracted power from the AC system, and i I is the current flowing through the inverter transformer.Assuming that the power and voltage reference values of the DC network are consistent with the AC system, the basic equation of the inverter in per unit is: Generally, the control mode of the DC system converter needs to be determined.The B787 mainly adopts the converter control mode of constant transformation ratio, constant control angle, and constant power.In this paper, the converter control mode of constant transformation ratio and constant control angle is adopted.

The mathematical model for the OPF in MEA 2.2.1 Objective function.
The objective of the optimal power flow problem for AC/DC systems of MEA is to minimize the active power loss of the whole system: That is, all active loads used are subtracted from all active power produced in the entire network.

Constraints
Power flow constraints of the system: Converter constraints include the DC network equation and the introduction of the control mode equation: Generator constraints mainly include borders for generator output: Security constraints include voltage constraints, phase angle constraints, and branch transmission power constraints for all nodes: .min .max.min.max.min.max

S S S
DC side constraints mainly refer to the voltage, current, converter ratio, and power factor angle of the converter: . min .max . min .max The number of variables is 5 di n , the number of equations for the DC system is also 5 di n , so the system can be solved.

Interior Point Method
The OPF problem can be expressed as the following nonlinear optimization model: [ ,, , , ,,,,] is included.Compared with a pure AC system, five DC variables of the converter are added.In the equation, ()  hx is equality constraint, () gx is inequality constraint.The central parameter of the PDIPM method is usually fixed.In many practical problems, the central parameter does not point to the fastest convergence direction, which may lead to the fact that multiple iterations do not play an obvious role in the convergence of the algorithm.The core idea of PCPDIPM is to dynamically estimate the central parameter so that the direction the central parameter points to can always find the optimal solution as soon as possible.
Compared with the OPF of AC system, the Jacobian matrix of OPF of AC and DC system has the characteristics of dimension expansion and complex structure.Dimension is extended from .The increase of the Jacobian matrix for power flow calculation is shown in Equation ( 11 The power flow calculation can generally adopt the unified iterative method and the alternating iterative method.The first method has a good convergence, so the unified iterative method is chosen for power flow calculation.For the quantity that has been given a fixed value by the converterspecified control mode, its fixed value is directly taken as a constant, and the transformer ratio itself is a discrete variable, which is treated as a continuous variable during calculation.

B787 power system analysis
The B787 power system adopts two frequency conversion starting generators installed on each of the two main engines.Each generator supplies power for its own 235VAC bus.Three power conversion devices are used to convert 235VAC to other types of power, to satisfy the demand of most aircraft loads.Figure 3 is the main load connection diagram of the B787 power system.To quantify the cable length between different nodes, the information shown in Figure 4 is combined with the size of Boeing 787 aircraft.The aircraft is considered as a plane, and the straightline distance between different systems is taken as the actual length of the cable to estimate the node distance.

B787 power system analysis
The active power loss before and after optimization under seven flight states is given in Table 2.The example results show that the interior point algorithm can solve the OPF problem of the AC/DC system well.From the table optimization results, it can be seen that the power loss is reduced by more than 10%, and it can converge well under various control modes.The interior point algorithm shows the characteristics of periodic convergence.When it converges to the neighborhoods of the optimal solution, it will enter the fast convergence stage until the algorithm converges completely.The iteration times of PDIPM and PCPDIPM in seven flight states are shown in Figures 5 and 6.Compared with the PDIPM, the PCPDIPM has obvious advantages in the number of iterations.Under the same conditions, the predictor-corrector interior point method only needs to increase a small amount of calculation of the prediction step and the correction step in each iteration, but the number of iterations can be reduced by 30% or more.

Conclusion
In this paper, the mathematical model of the optimal tidal current of the AC/DC hybrid system of MEA is established, and the optimization of the aircraft power system is realized through calculation.In this study, firstly, the power system of MEA is modeled.Then two interior point methods are used to calculate and optimize the model.Taking the B787 simplified power system as an instance, the OPF is calculated and tested, and the feasibility of the proposed model is verified.The significance of this study is to provide an effective method to establish the OPF model of MEA and carry out the corresponding calculation and optimization.This will help the design and operation of aircraft power systems, and promote the sustainable development of the aviation industry.

Table 2 .
Power Loss Before and After Optimization.

Table 3 .
The DC variables of the converter before and after optimization in the cruising state are shown in Table3.For DC lines, since the control mode of constant transformation ratio and constant control angle is adopted, d Table of Changes of DC Variables Before and After Optimization. 6