*Rectifiers are the most common nonlinear loads encountered in electrical power systems. Uncontrolled rectifiers are cheaper than synchronous rectifiers and more common than them because of this but the currents drawn by uncontrolled rectifiers contain harmonics. In addition, the amplitude of these harmonics depends on the value of the load power and the rectifier parameters. A 3-phase cable can be used to connect a three-phase rectifier to a 3-phase power system. In this study, the power losses of a 3-phase cable fed by a synchronous rectifier and an uncontrolled rectifier were compared. The electrical equivalent of a power cable is frequency dependent. The analysis performed in this study was made by making some assumptions about the frequency-dependent resistance of the cable and the rectifier currents. The analysis shows that when an uncontrolled rectifier is fed by a power cable, the cable always has more loss and heats up more for the same amount of RMS current.*

### 1. Introduction

Electrical resistance is a function of frequency [1]. Skin-depth results in extra power loss in a cable excited with AC currents [2, 3]. Three-phase cables are complex systems to model [4]. Such transmission line models can also be made with fractional-order circuit elements [5]. This results in higher attenuation in high frequencies [3, 5, 6]. Such a frequency modeling of the cables may require machine learning [6]. The effects of harmonics on underground power cables are examined by considering a real system and using experimental data and shown to result in an excessive temperature rise due to the power losses in the cable [7]. Aging processes such as water treeing, electrical treeing, and dielectric breakdown can be observed in polymeric insulators of cables [8] and the high-temperature operation of cables also contributes to their early aging [9-11]. Cable failures and degradations that may occur directly or indirectly in the cable due to harmonics should be prevented [11, 12]. Skin and proximity effects in the cable impedance are difficult to model [13]. Their accurate modeling is also important in motor drive applications [14]. Three-phase power cables are often used to feed power rectifiers in industry. An experimental model of such a rectifier can be found in [15]. Uncontrolled rectifiers are nonlinear circuits, which lack exact analytical solutions [16] and are hard to model. That’s why simplified models are often used in their analysis [17]. Some rectifiers use A frequency domain model for uncontrolled rectifiers as presented in [18]. A rectifier model for active loads is given in [19]. Averaging can also be used to model uncontrolled rectifiers [20]. A matrix solution for their modeling is presented in the frequency domain in [21]. An equivalent circuit for a diode bridge that makes use of AC and DC side rectifier harmonics is given in [22]. The uncontrolled rectifiers draw non-sinusoidal currents and their current profile varies by the load power [16-22] and this can cause overheating in the power cables. In this study, a lower bound for the power loss of a three-phase power cable feeding a three-phase uncontrolled rectifier is given to find out whether the loss stays the same for the same amount of transferred power to the load and whether the loss stays within the standards such as the international electrotechnical commission IEC 60287 standard [12].

The paper is arranged as follows. In the second section, the simplified models of an uncontrolled rectifier and a synchronous rectifier are given. In the third section, a lower value of the loss of power cable for an uncontrolled rectifier is given. The paper is finished with the conclusion section.

### 2. The Synchronous Rectifier and Uncontrolled Rectifier Modelsex

A three-phase synchronous rectifier is a power electronic circuit, which uses the three-phase H-bridge inverter topology shown in Figure 1.a. Such rectifiers make use of sophisticated switching control strategies to withdraw almost sinusoidal currents from a three-phase utility with almost a power factor of one [23-26]. Since the harmonics around switching frequencies have very low magnitudes [27], their phase currents can be expressed as

(First Author’s) Surname et al. / European J. Eng. App. Sci. 6(1), 19-24, 2023

where 𝐼𝑚 is the maximum value of the phase currents and 𝜔 is angular frequency.

The three-phase phase voltages can be written as

where 𝑉𝑚 is the maximum value of the phase voltages.