# Reactance Regulation Using Coils with Perpendicular Magnetic Field in the Tubular Core design
## 1 Introduction  
In the present day, the consumers look to additional energy generation facilities (e.g., solar, wind) to fulfill their increasing energy demands [1; 2; 3; 4; 5; 6]. Renewable energy produced by consumers can be utilized for themselves and can also be transferred as surplus energy to the distribution grid. Such consumers are termed as prosumers [7]. The electrical power generation from renewable energy sources is not always steady as it depends on environmental conditions [8]. Hence, efficient and accurate analog control is required. Such control should equalize the energy flow balance between prosumer needs and its generation ability by regulating power flows and prosumers in the distribution line [9]. Nowadays, several electronic control systems relate to the grid to monitor the real situation [10]. These systems determine the need to connect/disconnect load or to connect reactive power with the grid in case of voltage instabilities, shortening, or any other faults [11; 12]. The sluggish response of control systems restricts the flexibility and efficiency of energy flow regulation [13]. In this case, the analog connection seems more efficient. The controllable reactance can adjust the energy flow smoothly and rapidly in both directions [14; 15; 16; 17]. The magnetic amplifiers (MA) and magnetic circuits were widely used in power flow control systems [18; 19; 20]. These MAs are useful for numerous power systems because of several advantages, e.g., high temperature durability, reliability, simplified control circuit, good dynamic characteristics, and significant amplification effect [21; 22; 23; 24; 25; 26]. The MAs are widely used inpower distribution high voltage networks to control power flow and over-current protection [22; 23]. In direct-drive wind turbines, the MAs are also used for permanent magnet synchronous generator control [24]. It is observed that these amplifiers improve the ride-through capability of the permanent magnet synchronous generator [25]. The MAs can operate at high frequencies as compared to analogous circuitry based IGBT devices [26]. Therefore, MAs can be successfully used for significant power circuitry as well as for relatively small applications. Several geometrical arrangements for MAs were suggested to diminish the induction effect [27]. The induction effect exists because of the induction of the AC coil on the other one. The major drawback of MAs is the non-symmetry and appearance of the offset in the current curve. The main reason is the shift of the initial point on the magnetization curve. To prevent the non-symmetry an off-set current is applied to split current flow for two paths, one in positive and another in a negative direction by diodes [28]. This solution requires a double reactance arrangement, as a result the device becomes bulky. In this scenario, the design with two perpendicular and magnetically independent coils seems more convenient than others. Different methods were proposed and discussed to develop magnetically independent coils [26; 27; 29]. One design is based on the suggested antiparallel arrangement of two magnetic cores [26]. However, these devices are bulky as both coils are wound on different cores. [PERSON] et al. proposed a specific design of the MA using flat magnetic rings for superconducting energy storage [30]. The separated magnetic rings are placed in the toroidal direction over the internal winding. The air gap between magnetic rings is one of the significant disadvantages of such designs [30]. To avoid the air gap problem, the MAs are designed using the laminated magnetic core [31; 32]. The control coil is placed inside the laminated magnetic core. Our previous article discussed the advantages and disadvantages of the toroidal magnetic core with two perpendicular coils [33]. The simplistic design of MAs has benefits for modern applications. This article presents an efficient magnetic amplifier (MA) for the smooth connection of prosumers to the distribution line.