Unit vector template generator applied to a new control algorithm for an UPQC with instantaneous power tensor formulation, a simulation case study

Yeison Alberto Garcés Gómez1, Nicolás Toro García2, Fredy Edimer Hoyos3 1Universidad Católica de Manizales-Unidad Académica de Formación en Ciencias Naturales y Matemáticas, Colombia 2Universidad Nacional de Colombia-Sede Manizales, Department of Electrical and Electronics Engineering and Computer Sciences, Colombia 3Universidad Nacional de Colombia Sede Medellín Facultad de Ciencias, Escuela de Física, Colombia


INTRODUCTION
The UPQC are power electronic devices that act like controlled voltage and current sources in power systems so that it can remove or reduce the effect of power quality issues like harmonics, sags, swells, imbalances in power source or loads and also lead to improve the power factor [1,2]. The growing interest in UPQCs come from last century, and since the concept of "power quality" has been gaining increasing popularity in the field of electrical engineering, today, it has become a great topic for companies providing electricity service, equipment manufacturers and end users, that leading to solutions searching to solve the problems of power quality [3][4][5][6][7][8].
Regarding the estimation algorithms of reference signal, many theories and methods have been proposed to define the control signals to correct the problems of power quality either voltage or current, which highlights the use of the instantaneous active and reactive power theory or pq theory, as one of the theories most used in order to generate reference currents in the shunt active power filters and UPQC; while often the estimation of sequence components and phase-looked-loops "PLL" are used for the voltage reference estimation and the grid synchronization with the filters, respectively [9,10].

INSTANTANEOUS POWER TENSOR FORMULATION
The tensor formulation of instantaneous power proposed by Herrera et al [18,19], and thereafter defined like "Instantaneous Power Tensor Theory" by Ustariz et al [20,21], is based on the interpretation of the instantaneous voltage and current vectors like first order tensors, and then to define the power components by the dyadic product in a n-phase system, and proposing compensation models for the same type of system. From vectors �⃗ = = [ 1 2 ⋯ ] an⃗ = = [ 1 2 ⋯ ] d Herrera et al., [18,19] defines the active power ( ) and the imaginary power ( ) like: where, ∧ denotes the outer product, that is an antisymmetrization of dyadic product denoted by the operator ⊗, so that: besides the components of the current is defined as follows: expression equivalent to: Moreover, the total current demand for the load is expressed as: Finally, the decomposition of the current leads to the expression (7): The power and current components defined by Ustariz [20,21] are self-same to Herrera, although the development of Ustariz shown at a slightly form more elegant the tensorial formulation from the definition of the instantaneous power tensor ℘ in (8). Thus, for an n-phase system, the instantaneous power tensor is given by: from (7 and 8), Ustariz performed the decomposition of one instantaneous power tensor in two, called active power tensor ( ℘ ) and reactive power tensor ( ℘ ), like in (9): finally, the current components are defined as follows: becoming clear, the expressions in (10 and 11) by Ustariz are the same as defined in (5 and 6) by Herrera.

SHUNT INVERTER CONTROL ALGORITHM
From the tensor formulation [18][19][20][21], several tech-niques have been proposed for compensation in shunt active filters, one of these is the technique of the perfect harmonic cancellation "PHC" at source. Estimation of reference for this control strategy for the active filter is given by: in (12), ⃗ _ + is the direct sequence and fundamental frequency, active instantaneous current vector, defined by: the expression (13) proposed by Ustariz et al, is equivalent to (14) proposed by Herrera: where is the average norm of the voltage instantaneous vector, and = (℘ � ) is named like average active power by Herrera or average instantaneous power tensor by Ustariz. Block diagram for current reference estimation by PHC technique is shown in Figure 2 [21]. For compensation of the reactive power at a fundamental frequency, the algorithm described in Figure 2 makes use of a block called "DSFC" (direct estimation algorithm sequence fundamental frequency) for the load voltage [22]. This algorithm uses the inverse transform of Fortescue for determining direct sequence and trigonometric operations for extracting the fundamental frequency defined by the fast Fourier transform. The algorithm supports wave forms unbalanced and non-sinusoidal, but unfortunately, the algorithm does not support sags and swells in voltage. It has been verified by simulation that, in voltage sags, the algorithm decreases proportionally the reference current, and therefore, does not have the expected complete compensation.

SHUNT INVERTER CONTROL ALGORITHM
As mentioned in the previous section, the PHC algorithm reported in [22] is not tolerant to variations in the power supply, such as sags and swells, which is why this algorithm has been modified to make it tolerant to these perturbations. The modification to the referenced, uses template generation unit vector (UVTG) for obtaining direct sequence voltages and fundamental frequency and a PLL in the synchronous reference system (SRF-PLL). The "UVTG" technique is well described in [23][24][25].
Extracting reference signals from the PLL and SFR-UVTG technique is sufficient to extract the reference signals of the active filter in series UPQC-DG inverter. In Figure 3 the complete diagram estimation references for unified power quality conditioner is illustrated. The voltage reference is set at (15).
In the diagram of Figure 3 the "UVT" block provides sinusoidal signals at unit value in phase with the fundamental component of the source voltage independent of its magnitude or harmonics condition.

NUMERIC SOLUTION AND RESULTS
The simulation corresponding to the algorithm regarding the generation of the reference was imple mented in Matlab-Simulink®. The model has a voltage source distorted with harmonics for feeding a nonlinear load with a given current displacement factor to ensure control of the reactive power, the supply voltage is also applied to the system at some point of a voltage sag to verify that the algorithm is tolerant to these Figure 4. The inverters control loop has been made by hysteresis with fixed switching frequency [26,27] with the same frequency in both switching inverter bridges, the model implemented for this control is illustrated in Figure 5. The first part is the error which is passed through a system that converts the error to binary values as stated in (16): Although the switching output of boolean type, is variable and depends on the dynamics of change in the measured error, in the D-type flip-flop, switching frequency is fixed at a constant value given by the block sequence (serving as clock) and can be set according to the inverter's design criteria. Although the literature has reported many methods of controlling inverters, we have implemented this model because it has a quick  In Figure 6, the waveform of one phase of the power supply and the RMS value over time of simulation are illustrated, it is heavily contaminated by harmonics, illustrating the effect of distorting the current loads on source impedances. Furthermore, a voltage sag of three cycles is shown to verify that the algorithm can compensate for such transients on the network. In this case we have simulated a drop in the RMS value of 30 %.
The UPQC is operated in four time intervals: in the first 3 cycles is not given compensation in voltage or current, in the second time interval, beginning at the 4rd cycle, the voltage compensation is only activated, in this range the series active filter compensates harmonics, isolating the load Figure 7. At the point where the voltage dip is generated, it is observed how the compensation voltage of the series filter increases to make up for the drop. In the next interval, from the 6 th cycle, compensation of harmonics and reactive power in current is activated, in this case, the parallel inverter injects the compensation current needed to eliminate harmonics generated by the load and to carry the power factor to the unit. In the signals of reference can be seen that the length of the voltage sag time is compensated by an increase of the voltage signal reference.