INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING DOI: 10.46300/9106.2020.14.35 Volume 14, 2020 Circuit Theory Analysis of Parity-Time-symmetric Wireless Power Transfer System Yu Jin, Wangqiang Niu, Wei Gu Key Laboratory of Transport Industry of Marine Technology and Control Engineering, Shanghai Maritime University, Shanghai 201306, China Received: April 16, 2020. Revised: June 11, 2020. 2nd Revised: June 17, 2020. Accepted: June 18, 2020. Published: June 19, 2020. WPT system [1], [2]. To implement continuous and efficient Abstract—Wireless power transfer (WPT) technology power transmission, four common types of WPT technology reduces the risks brought by connection between electrical are introduced: magnetic resonance WPT (MRWPT), equipment and power source, it has been widely used in inductive WPT (IWPT), microwave WPT (MWPT) and laser various fields in recent years. To overcome issues of low WPT (LWPT). Nevertheless, the IWPT system may have an transfer efficiency and poor robustness when coupling adverse effect on people or things in two coils; the transfer coefficient varies, a WPT system based on parity-time (PT) efficiency of MWPT is relatively low [3]; the cost of LWPT is symmetric circuit is proposed, which consists of two RLC much more than other methods. So researches more focus on oscillators. The system state equation is obtained by circuit the MRWPT method [4]-[7], which has a strong theory, then be analyzed to derive the system resonance anti-interference ability to the surrounding environment. The frequency, transmission efficiency, and phase difference phenomenon of frequency bifurcation appears in the MRWPT between Tx and Rx. A simulation based on PSIM is system in the strong coupling region, resonance frequency of established to verify the theoretical derivation of transmission system varies when the variation of coupling coefficient, the characteristics. The simulation results illustrate that the operating frequency of the system does not adjust resonance frequency of the WPT system is adjusted automatically in the strong coupling region when the coupling automatically with the resonance frequency, which causing a coefficient changes, the output voltage across the load constantly changing transfer efficiency.. This phenomenon resistance always equals source voltage on the transmitter. was demonstrated in [8] and concluded that the maximum load Compared with the non-parity-time symmetric system, power could be obtained at the frequency bifurcation point. PT-symmetric WPT system could achieve higher transfer Reference [9] established a circuit model and made an exact efficiency over a longer distance, this scheme can transfer explanation for the frequency bifurcation phenomenon. The power with constant efficiency of over 80% in a certain further analysis of contactless power transfer characteristics region. A set of simulations with variation load resistance are with relay coils was studied in [10] using coupled mode theory considered to verify the system robustness. All results are and practical experience, which concluded that the type of consistent with theoretical derivation and analysis. frequency bifurcation changes with the number of relay coils. To obtain higher and constantly transfer efficiency, the Keywords—Wireless power transfer; Parity-time-symmetry; operating frequency of WPT system should track the resonant Circuit model; Power transmission characteristics. frequency. References [11]-[14] analyzed the output power I. INTRODUCTION characteristics of WPT system to obtained optimal solutions, IRELESS power transfer (WPT) technology has been then a negative feedback control module was designed to track W extensively used in various occasions, such as mobile specific parameters at the transmitter or receiver, such as the devices and electric vehicles, autonomous underwater vehicles mean value of current sampling on the transmitter at the (AUV) and automated guided vehicles (AGV). It is greatly voltage commutation point [15]. Frequency tracking detuning improving the flexibility of electrical equipment, makes the control strategy based on the differential link phase-locked repair of the faulty device easier. However, low transfer loop was also commonly used to implement constant power efficiency and poor robustness are two main issues of the transfer [16]. References [17] and [18] offered reactive power compensation for contactless power transfer systems with variable load. Reference [19] pointed out a situation that ISSN: 1998-4464 241 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING DOI: 10.46300/9106.2020.14.35 Volume 14, 2020 non-resonance maximizes the efficiency of power of WPT system by coupled mode theory, the relationship transmission, considering both output power and efficiency, between the energy model and coupling mode was discussed, then decide a balanced working frequency under the condition the mathematical significance of their equivalence is studied, of resonance is different with the maximal efficiency. ultimately, simulations based on MATLAB were used to Feedback mechanisms and compensation mechanisms were verify the theoretical analysis. Current and voltage are the utilized to achieve efficient power transmission. The shape main parameters in WPT system and easy to understand in the and structure of WPT system also affect transfer efficiency. A field of electronics, so circuit theory method is utilized in this novel meander-type laminated coupled structure was proposed paper. This paper analyzes the characteristics of WPT in [20], with higher transmission efficiency and output power. system based on PT-symmetric circuit by circuit theory The above researches achieved efficient power transmission method, which focuses on the amplitude, phase and waveform by utilizing an additional feedback loop, but the poor real-time of output voltage on transmitter and receiver. Variation of performance and high cost were also should be regarded. transfer efficiency and operating angular frequency during The PT-symmetry principle was originated from quantum resonance is also expressed in this paper, and simulations physics. The first experiment of PT-symmetric circuit was demonstrate the accuracy of theoretical model. A comparison performed by Professor J Schindler of Wesleyan University in between PT-symmetry WPT system and Non-PT (NPT) 2011, the experimental circuit structure consisted of a pair of symmetry WPT system on the above characteristic is given, coupled LRC oscillators. The transmitter contained a that verify stability and efficiency of PT-symmetry principle nonlinear gain whereas the receiver had the same amount of applied to WPT system. The remaining of this paper is attenuation, which offered the simplest implementation of a organized as follows: Section II expresses the theory of PT-symmetry system in the electronic field [21]. Then PT-symmetry, circuit theory model，theoretical analysis of Professor J Schindler established PT-symmetric dimer modes PT-symmetric characteristics in WPT system. Simulations to express all universal phenomena encountered in systems based on PSIM verify theoretical derivations in Section III. with generalized PT-symmetric in the next year [22]. In 2017, Finally, Section IV concludes the paper. Professor Fan of Stanford University applied PT-symmetric circuit to WPT system [23] and successfully lighted up a 60 W II. MATERIALS AND METHODS lamp in 2 meters, achieved robust against variations in distance. Reference [26] proposed a new dual-coupled robust A. Theory of Parity-Time-Symmetry WPT model based on the PT-symmetry principle of [24] to The parity-time-symmetry is a property described by the implement efficient and stable power transmission. invariance of parity-inversion and time-inversion. This theory Considering the applications of PT-symmetry WPT system, has been used in optics, high energy physics and field theory, [25] and [27] applied PT-symmetric circuits to charge fuzes WPT system has familiar transmission principle with optical with variable gap and wireless charging for drone systems, coupling application, that is the reason why PT-symmetric respectively. A research on the transmitter amplification of theory could be used in WPT system. Parity-inversion is negative resistance based on PT-symmetry principle was defined by the inversion of space, in continuous space presented in [28], that summed up the amplification was coordinates. Parity-inversion means mirroring from the space adjusted automatically with varies distance. An ultra-sensitive coordinates of x ↔ -x. Similarly, the odd powers to x and their sensor based on parity-inversion and time-inversion was odd derivatives also have corresponding mirroring properties proposed in [29], which could detect changes of resistance or [13]. Time-inversion indicates the reversal of time direction, reactance accurately in a circuit. References [30], [31] that is, t ↔ -t, the odd-numbered derivative of time t also analyzed the PT-symmetric circuits and transmission needs sign transformation. The PT-symmetric system is characteristics of WPT systems from the perspective of the realized by a symmetric circuit model with gain element and Duffing inequality, it also opened a new direction toward loss element. When the gain and loss of the system are same investigating novel analytical method for the PT symmetrical value with opposite sign, the energy flows steadily on both quantum system in WPT technology. sides of the system and then reach equilibrium. Nevertheless,