# Classic Discrete Control Technique and 3D-SVPWM Applied to a Dual Unified Power Quality Conditioner
## 1 Introduction  
Most efforts to improve power system operation are focused on using the most advanced technical solutions such as flexible AC transmission systems (FACTS) [1; 2], and for distribution networks, there is a wide variety of options that includes series and shunt compensators to improve power quality or reduce harmonics problems [3; 4]. Therefore, the unified power quality conditioner (UPQC) is considered as a good solution because it gives versatility when compensating several problems simultaneously [5]. An UPQC consists of two power inverters operating as active filters that share the same direct current (DC) bus [6; 7; 8; 9; 10; 11]; and they are widely used as energy controllers [12; 13; 14; 15]. The active power filters (APFs) are connected to the power system generally by means of coupling inductors for the shunt active power filters (shunt APF), and coupling transformers for the series active power filters(series APF). Both the shunt and the series inverters operate as controlled voltage or current sources in the system, mitigating the effects of power quality problems such as voltage and current harmonics, voltage sags, momentary voltage swells, flicker, unbalanced source, and unbalanced load. The schematic diagram of the UPQC is presented in Figure 1[16; 17; 18], where the series and shunt APFs are used to improve the harmonics. The term \(i_{it}\), \(i_{lb}\), and \(i_{ic}\) are the currents of the main electrical circuit that considers the source and load, which is supplied through phases a, b, and c, respectively; \(R_{rda}\), \(R_{rdb}\), and \(R_{rdc}\) are the resistances of the power grid in phases a, b, and c, respectively; \(L_{rda}\), \(L_{rdb}\), and \(L_{ndc}\) are the inductances of the power grid in phases a, b, and c, respectively; \(V_{B}\) is the DC link voltage; \(C_{b1}\) and \(C_{b1}\) are the corresponding capacitors in the DC bus; \(i_{csa}\), \(i_{csb}\), and \(i_{csc}\) are the currents of the series APF in phases a, b, and c, respectively; \(i_{rqu}\), \(i_{cbp}\), and \(i_{cpc}\) are the currents of the shunt APF in phases a, b, and c, respectively; \(L_{sa}\), \(L_{sb}\), and \(L_{sc}\) are the inductances of the series APF in phases a, b, and c, respectively; and finally, \(L_{pa}\), \(L_{pb}\), and \(L_{pc}\) are the inductances of the shunt APF, in phases a, b, and c.  
The traditional topology and the dual topology of the UPQC have identical devices in their circuit configuration, as shown in Figures 2 and 3. Thus, the traditional topology of the UPQC considers a series of APF that work as a controlled voltage source and a shunt APF that works as a controlled current source (see Figure 2). On the other side, the filters in the dual topology of the UPQC are interchanged and now the shunt APF works as a controlled voltage source and the series APF works as a controlled current source [19; 20; 21; 22; 23] (see Figure 3); where the terms \(v_{f}\) and \(i_{f}\) are the controlled voltage and current sources of the APFs, respectively. Figure 1: Diagram of power quality unified conditioner (UPQC). Figure 2: UPQC in traditional topology. The main advantage of the dual topology of the UPQC lies in the loop control of the inverters. In the traditional UPQC model, the voltage and current reference signals are highly distorted, and consequently, the control effort in power devices is considerable when trying to generate these distorted waveforms. On the other hand, in the dual UPQC, the compensation voltage references are pure sinusoidal, which allows a less demanding in the inverters in terms of switching frequency. The use of UPQCs in distribution networks and their performance analyses are widely found in the literature. For example, in [24] the authors verify the static and dynamic performance of the power quality conditioners PQC operating as UPQC.