Power quality investigation of a solar PV transformer-less grid- connected system fed DVR

Abstract

This paper presents a single stage transformer-less grid-connected solar photovoltaic (PV) system with an active and reactive power control. In the absence of active input power, the grid-tied voltage source converter (VSC) is operated in a reactive power generation mode, which powers the control circuitry, and maintains a regulated DC voltage to the VSC. A data-based maximum power point tracking (MPPT) control scheme which performs power quality control at a maximum power by reducing the total harmonic distortion (THD) in grid injected current as per IEEE-519/1547 standards is implemented. A proportional-integral (PI) controller based dynamic voltage restorer (DVR) control scheme is implemented which controls the grid side converter during single-phase to ground fault. The analysis includes the grid current THD along with the corresponding variation of the active and reactive power during the fault condition. The MPPT tracks the actual variable DC link voltage while deriving the maximum power from the solar PV array, and maintains the DC link voltage constant by changing the modulation index of the VSC. Simulation results using Matlab/Simulink are presented to demonstrate the feasibility and validations of the proposed novel MPPT and DVR control systems under different environmental conditions.

Graphical abstract

Keywords

data-based maximum power point tracking (MPPT) / total harmonic distortion (THD) / proportional integral / control / voltage restorer / pulse width modulation

1 Introduction

Custom power devices, like dynamic voltage restorer (DVR), a series active power filter is the latest development of interfacing devices between the distribution system and consumer. These devices overcome voltage and current disturbances, improve power quality by compensating the reactive power, and reduce harmonics generated or absorbed by the load. In the grid-connected PV system considering the power quality, studies on the line frequency transformer type are in progress, but studies on the transformer-less type are limited. One of the major problems in such systems is the increase in total harmonic distortion (THD) of the current injected into the grid during low solar radiation periods. Standards, such as IEEE-519/1547, stipulate that a current with a THD greater than 5% cannot be injected into the grid by any distributed generation (DG) source. The scope of the work presented in this paper is to introduce a model based analytical approach to design a suitable transformer-less, three-phase grid-connected inverter for solar PV applications. The role of custom power device, integrated with its control scheme, in the main system is also highlighted with simulation results.

Discussion is done to mitigate voltage sag and swell using proportional integral (PI) controlled DVR which provides the most effective solution by establishing the proper voltage quality level [1,2]. A control approach is presented which is based on hysteresis voltage with fuzzy logic and compensates network faults. It also mitigates their effects at different loading conditions [3]. THD, as per IEEE-519 standard, is also calculated (0.12%, 0.2%, 0.17%, and 0.16%) [4]. Capabilities of space vector control approach and multilevel VSC controlled DVR with low pass filter, which is used to mitigate the voltage sag and swell in a 22 kV distribution system is proposed [5]. A new pulse width modulation (PWM)-based control scheme is implemented to control electronic valves for a 2-level voltage source converter (VSC) controlled DVR [6]. During unbalanced fault conditions, the behavior of PI and proportional resonant (PR) controllers is addressed along with the corresponding variation of the active and reactive power during single-phase to ground fault [7]. An optimal utilization of a solar PV farm operating nighttime, as static compensator (STATCOM), which regulates the distribution voltage at point of common coupling (PCC) within utility specified limits (± 3%) is proposed [8]. Power quality characteristics of 13 PV inverters with rated power from 1 kW to 5 kW is analyzed, which shows that voltage harmonics depends on the actual phase angle of the injected harmonic current [9,10]. Using fast Fourier transform (FFT) analysis, a second order active Butterworth filter is used between VSC and utility grid to eliminate THD [11]. Line voltage THD is reduced from 32.59% to just 1.59% as per IEEE-519 standard. Two controllers, reactive power control (RPC) and adaptive predictive current controller (APCC) are used for single-stage grid-connected solar PV system in which reference current is calculated and current with THD (<5%) is injected into the grid through APCC and VSC [12]. The localized spectral analysis approach is applied to solar irradiance and derived quantities which determine power content of fluctuations, and power flow calculations [13]. The system is controlled for current harmonics, voltage sag-swell, and reactive power compensation by using a converter as an active series-shunt filter [14]. Power quality issues of voltage flicker, harmonics, and transient voltage are simulated and the system performances with and without STATCOM compared, and analyzed [15].

This paper describes the design and simulation of a novel high performance power conditioning system (PCS) for a solar PV three-phase grid-connected system, and its control schemes. The control schemes include a single-stage three-phase three-level transformer-less VSC and a PWM controlled [4] DVR. The model of the proposed solar PV array uses theoretical and empirical equations together with the data generated through the unique data-based maximum power point tracking (MPPT) control technique at variable temperatures, and solar radiation among other variables. The MPPT technique with the PI controlled DVR provides distortion-less maximum active power from the PV array, with negligible fluctuation of DC bus voltage to VSC, and fast tracking of optimum operating point at unity power factor at faulted conditions. This technique is comprised of a current voltage control in synchronous rotating d-q frame. The simulation of DVR is found quite satisfactory to eliminate unbalance voltage sag and swell. The DVR control scheme also shows simultaneous exchange of active and reactive power with the distribution system during fault. Finally, using the FFT analysis of calculated THD values of grid injected current as per IEEE-519/1547 standard and VSC current are shown to be approximately 6% and 8% respectively, which proves the correctness of the implemented control scheme. The results and their validations for the solar PV grid-connected system with the implemented MPPT but without DVR are also reported [16]. The validation of the model and the algorithm of the control systems is conducted through computer simulations using SimPowersystems of Matlab.

2 Solar PV grid-connected PCS

The primary units of the PCS system shown in Fig. 1 are an array of solar PV panels modeled as described in Refs. [17,18], an insulated gate bipolar transistor (IGBT)-based VSC, and a three-phase interfacing reactor-capacitor-reactor used as an LCL-filter. The solar PV array is connected parallel to the IGBT-based VSC through a DC-bus capacitor [19]. The AC-side terminals of the VSC are connected to the PCC through an interfacing LCL-filter, Fig. 2. The parallel capacitor of the LCL-filter prevents the current harmonics produced by the inverter-based DG system from infiltrating into the distribution network side. A 3-\phi series RLC load is connected between the main grid, and the IGBT-based VSC.

2.1 Power system configuration

Most of the works in literature survey are based on a two stage conversion system, one DC/DC and the other, DC/AC (or VSC) converter. However, in the present work, only one conversion stage is considered which is used for controlling the PV array voltage and delivering energy to the grid at a maximum efficiency. Five algorithms which are simulated to control the power generation are the MPPT, phase locked loop (PLL), current control, sinusoidal pulse width modulation (SPWM) [4,20], and DVR control system.

Based on the block diagram of the overall system shown in Fig. 1, the control systems are implemented to have a pure sinusoidal current with less THD at unity power factor and the DC voltage to the VSC is maintained constant. An LCL-filter, connected between the VSC and the grid, converts the voltage generated by the VSC to current, reduces high frequency switching noise, and protects the VSC from transients. A three-phase discrete PLL is employed in order to track the angular frequency and phase shift of positive-sequence components of three-phase voltages for synchronization. For a three-phase sinusoidal signal, an abc to dq0 rotating reference frame transformation is applied [21] which generates currents I_d and I_q.

2.2 Real and reactive power control

Typically the IGBT VSC efficiency is very high. In absence of active input power, the grid-tied converter is operated in a reactive power generation mode which powers the control circuitry, compensates the converter losses, and maintains a regulated DC voltage. With simulation results, it is shown that when the active power is not available, the DC link capacitor is charged, and voltage is kept within limits while injecting the desired level of the reactive power into the grid. Using power transfer theory [22], the real power and reactive power flow can be expressed, respectively as

(1)P={\displaystyle \frac{V_{inv}^2}{Z}}\cos \phi -{\displaystyle \frac{V_{inv}}{Z}}{V}_g\cos (\delta -\beta +\phi ),

(2)Q={\displaystyle \frac{V_{inv}^2}{Z}}\sin \phi -{\displaystyle \frac{V_{inv}}{Z}}{V}_g\sin (\delta -\beta +\phi ).

For the unity power factor operation at the grid,\beta = 0, assuming R is very small for only inductive coupling, \phi≈90°, Z= jX, Eqs. (1) and (2) become

(3a)P={\displaystyle \frac{V_{inv}}{X}}{V}_g\sin \delta ,

(3b)Q={\displaystyle \frac{V_{inv}}{X}}(V_{inv}-V_g\cos \delta ).

Converter current,

(3c)I_{inv}={\displaystyle \frac{\sqrt{\mathrm{2}}\sqrt{P^{\mathrm{2}}+Q^{\mathrm{2}}}}{V_g}}.

From Eq. (3), it is found that the real power mainly depends on angle \deltawhereas the reactive power depends on V_{inv}. A positive value of real power implies feeding active power into the grid while a negative value results in drawing power from the grid.

2.3 Sinusoidal pulse width modulation

SPWM [23] is one of the most popular modulation techniques among others applied in power switching inverters. In this technique the output voltage (line to line) as obtained in linear modulation range is given by

(4)V_{AB}=V_{BC}=V_{CA}=m{\displaystyle \frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}{V}_{dc},

where m≤1.0, for linear range. In the SPWM switching technique, the magnitude and phase angle of voltages at inverter output directly depend on modulation index and its phase angle.

3 Control system techniqtues

In this paper, a solar PV array [17,18,24] (consisting of six modules) is based on single-diode equivalent circuit. In DG systems [25], all available electric power is delivered to the grid. To achieve this, the PV system needs a control system that senses variations in the PV array condition, and leads the system to a new operating point (V_mp and I_mp), called maximum power points, where the maximum power can be extracted. The main controlling techniques have been found to be, Perturb & Observe (P&O) or dithering [20,26], incremental conductance (IC), constant voltage [21], fuzzy level control, neural network, and ripple correlation factor [14,15,17]. However, a data-based MPPT technique [16] is implemented in Section 3.1, which can efficiently generate PV power even under changing weather conditions. The proposed technique is a simple approach with low calculations which takes series resistance effect of the PV cell with model mismatch under changing environmental variations. In Section 3.2, with application of fault on grid side, this MPPT technique with DVR control provides distortion-less maximum active power from PV array, with negligible fluctuation of DC bus voltage to the VSC.

3.1 Data-based MPPT technique (Proposed one-first control scheme)

A unique method of data-based MPPT technique is developed due to its easier implementation. This technique, although simple, produces satisfactory results, being even more efficient for low intensities of solar radiation than most widely used two techniques (P&O and IC). Using the proposed technique, the maximum output power and substantial control and increase of the output power of PV arrays in solar PV generation system can be achieved. In this technique, the data given in Ref. [16] is used which have been generated using six solar PV modules forming an array. Each module is simulated at different solar radiation level and temperature values as per arrangement, as demonstrated in Fig. 3 (at particular cell temperature T_c). The data, thus generated, at maximum power is tabulated in Table 1. The power-voltage characteristics [27], thus obtained, through the simulation model for one particular set are displayed in Fig. 4. It is found that the output voltage decreases linearly when the series resistance and temperature increases. The output power of a single PV module depends upon the output voltage, temperature and solar radiation level. From Table 1, four data sets are formed through using four different cell temperatures showing model mismatching which includes variation of solar radiation levels, and temperature throughout the day. Using power-voltage characteristics, the PV module voltage is chosen at the maximum power point for a particular solar radiation level at a specific cell temperature. Table 1 lists the data thus finally simulated through look-up table (with its solving method Interpolation-extrapolation). In addition, a temperature selector switch is used in the simulation model for selecting the data in desired temperature range (T_c range 10°C−40°C).

The DC link voltage is controlled as per simulated voltage control scheme depicted in Fig. 5. The data (at different solar radiation and temperature) for the PV module voltage at a maximum power is selected to generate reference signal V_{dc_Ref}. Using the DC voltage regulator exhibited in Fig. 6, this signal is compared with the actual DC link voltage V_dc to generate error signal I_{d_Ref}.

To control the reactive power, a quadrature axis reference current is generated from the load connected and the grid side at unity power factor. This signal is compared with the actual quadrature axis current from the inverter side to generate an error ∆I_q. Similarly, a direct axis reference current is compared with the actual direct axis current of the inverter to generate an error ∆I_d. Two error signals are given to PI controllers (inner current controlled loop of Fig. 5) through which the error signals are converted into V_d and V_q. The modulation index m_a and angle δ are calculated using Eqs. (5) and (6).

Modulation index:

(5)m_a=\sqrt{V_d^{\mathrm{2}}+V_q^{\mathrm{2}}},

Angle:

(6)\delta ={\tan }^{-\mathrm{1}}\left({\displaystyle \frac{V_d}{V_q}}\right).

Substituting Eq. (5) into Eq. (4), it is seen that the inverter output voltage can be changed by changing the modulation index of the inverter. When the output voltage of the inverter is higher than the grid voltage, the reactive power is supplied by the PV system to the grid. However, the same gets absorbed when inverse action takes place.

3.2 Series voltage controller-DVR (second control scheme)

The basic function of medium voltage DVR is to inject a voltage component of desired amplitude, frequency and phase [5], between the PCC and the grid in series with the utility or load voltage, as shown in Fig. A1. The essential part for the well-performance of the controller in DVR is the sag-detection circuit [3]. The voltage sag must be detected fast and corrected with a minimum of false operations. A forced commutated VSC is considered in the DVR along with energy storage to maintain the capacitor voltage. From Eq. (7), the three-phase supply is transformed from abc to positive, negative and zero sequence components [23].

(7)\left(\begin{array}{c}{V}_1\\ V\\ V\end{array}\right)={\displaystyle \frac{1}{3}}\left(\begin{array}{lll}1\hfill & a\hfill & a^2\hfill \\ 1\hfill & a^2\hfill & a\hfill \\ 1\hfill & 1\hfill & 1\hfill \end{array}\right)\left(\begin{array}{c}{V}_a\\ V_b\\ V_c\end{array}\right).

The aim of this second control scheme is to regulate and maintain grid voltage magnitude with the DC link voltage to the VSC (with MPPT) constant at a point where a sensitive load is connected with the solar PV grid system under system disturbances. The Simulink model shown in Fig. 7 and parameters given in Table 2, the PI controller input is an error signal obtained from the reference voltage and root mean square (rms) value of grid voltage as per Eq. (7). After processing, the PI controller generates angle β which controls the PWM signal generator. Simultaneous exchange of active and reactive power also takes place. The discrete PI controller processes error signal to generate the required angle to drive this error to zero so that the grid rms voltage V_g is brought back to reference voltage after application of fault. At fault, the grid voltage is measured by three-phase sequence analyzer which measures the rms voltage, and compensating voltage is injected on the grid side through a three-phase linear transformer. This action also controls the load and VSC voltage current values. Thus, by measuring the rms voltage at PCC, compensating voltage is injected on the grid side which also controls the load and VSC voltage current values.

The values of amplitude modulation and frequency modulation index are given, respectively, as

m_a={\displaystyle \frac{V_{cont}}{V_{tri}}}=\mathrm{1}pu,m_f={\displaystyle \frac{f_s}{f_{\mathrm{1}}}}={\displaystyle \frac{\mathrm{15000}}{\mathrm{50}}}=\mathrm{300.}

4 Results and discussion

To prove capabilities of the above mentioned control method, the solar PV grid-connected test system with its MPPT and PI controlled DVR is modeled with Matlab/Simulink and SimPowersystems [23]. All system parameters used in simulation for the solar PV and control system for VSC are tabulated in Table 3. A 3-\phi series RLC load is connected on the output side. With simulation results shown, the active power transfer takes place, reactive power is compensated, and DC voltage to VSC is maintained constant. Besides, the three-phase faulty grid voltage and current is controlled through the PI controlled DVR, among other controlled variables under faulted conditions.

Figure 8 shows the simulation results without DVR. A single phase to ground fault (on phase A) is created at PCC on the grid side. The fault and ground resistance values are 0.066 Ω and 0.001 Ω, respectively. From fault time 0.1 s to 0.4 s, the above wave shapes demonstrate unbalanced sag/swell in the current voltage of VSC, load and grid.

With the DVR control system connected in series with line, compensating voltage is injected rapidly into the grid side at PCC, and voltage sag is mitigated completely in three phases. This action also controls the voltage and current wave shapes of the load and VSC, and maintains a balanced constant voltage at 1.00 pu. Thus effective regulation with the rms voltage maintained at 98%, is provided by the DVR control system shown by wave shapes in Fig. 9.

Figure 10 (a) shows the real power being generated by the PV system through VSC at different solar radiations and temperatures during fault as per Table 1. Till 0.1 s, the solar PV array generates a real power of 37.79 kW through VSC. Due to the occurrence of fault between 0.1s to 0.4 s, the real power flow remains constant and after 0.4 s, the reactive power is supplied through VSC as the real power goes negative till 0.5 s. After 0.5 s, a reverse action takes place till 0.6 s. The irregular behavior of the active and reactive power, as shown in Fig. 10 (a)−(b), is mitigated when DVR is in operation, as shown in Fig. 11 (a)−(b). Initially, the whole real power is being supplied by the grid to the load (as shown by negative direction of real power flow). But, as solar radiation level increases, the PV system partially supplies 3-\phiload through VSC and the grid. The maximum value of the real power from the PV array through VSC is found to be 37.88 kW, 37.74 kW, 36.32 kW and 28.49 kW at 10°C, 20°C, 30°Cand 40°C, respectively, which indicates that the real power value output decreases with the increase in temperature. At around 0.02 s, there exists a transient overshoot of approximately 10 kW from the basic load level which has been controlled in 0.02 s, (called settling time t_s) by implementing MPPT in the control system. Thus the calculated value of exponential damping frequency σ_d (= 0.25 t_s) is found to be 0.005 s.

The maximum value of reactive power, Fig. 11 (b), from the PV array through VSC is found to be 26.26 kvar, 26.45 kvar, 26.08 kvar and 25.83 kvar at 10°C, 20°C, 30°C, and 40°Crespectively, which indicates that the wave shape of the reactive power remains almost constant with the increase in temperature, particularly after 0.12 s. Initially, the grid supplies the reactive power requirement of inductive load, however, at around 0.1 s, the reactive power requirement is completed by the PV array through VSC and continues till the end. The sag and swell from the PV array output current and voltage wave shapes, as shown in Fig. 10 (c)−(d), is also mitigated by the DVR control action, as shown in Fig. 11 (c)−(d).

When there is a change in solar radiation and temperature as per Table 1, the proposed MPPT control system operates by increasing/decreasing the current injected into the grid in order to keep constant the voltage at the PV array terminals in its maximum power point. Figure 12 (a), shows the actual DC link voltage not varying exactly according to the reference signal generated from the lookup table (Table 1). But the PI controlled DVR helps the PV array actual DC link voltage to track the reference signal, as shown in Fig. 12 (b). At the same time, the DC voltage regulator also helps the actual DC voltage to track the reference DC link voltage at different solar radiation S_x and temperature T_x. The tracking error of the reference voltage is found to be less than 5%.

As the grid voltage of the solar PV grid-connected system is controlled through the PI controlled DVR shown in Fig. 9 (e), its THD as per Table 4 at different cell temperature T_c is found to be less than 1% whereas the THD for the grid current is found to be approximately 6% as per IEEE-519/1547 standard. However, the THD of VSC current is found to be slightly high which is due to the high frequency switching of the VSC.

5 Conclusions

This paper has emphasized an approach of modeling and controlling of a grid-connected solar PV system in conjunction with a PI controlled DVR (a custom power device). The simulation of the two control systems has been done in Matlab-Simulink, which shows an excellent coordination of both VSC and its implemented MPPT with DVR controlled system during occurrence of dynamic fault. It has been found that there is negligible fluctuation of DC bus voltage, fast racking of optimum operating point, robustness of the PLL and achievement of a unity power factor. Simultaneous exchange of distortion less active/reactive power with the distribution system has also been shown, along with mitigation of voltage sag/swell during single phase to ground fault. The proposed MPPT has proved its utility in the optimization of PV power generation and performs power quality control to reduce THD currents as per standards IEEE-519/1547. The speed of response and robustness of both control systems has been shown through simulation results.

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