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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

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Volume 15, Issue 1

# Modeling and Simulation for an 8 kW Three-Phase Grid-Connected Photo-Voltaic Power System

Zhaohui Cen
• Corresponding author
• Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, a member of Qatar Foundation, P.O. Box 5825, Doha, Qatar
• Email
• Other articles by this author:
Published Online: 2017-09-26 | DOI: https://doi.org/10.1515/phys-2017-0070

## Abstract

Gird-connected Photo-Voltaic (PV) systems rated as 5-10 kW level have advantages of scalability and energy-saving, so they are very typical for small-scale household solar applications. In this paper, an 8 kW three-phase grid-connected PV system model is proposed and studied. In this high-fidelity model, some basic PV system components such as solar panels, DC-DC converters, DC-AC inverters and three-phase utility grids are mathematically modelled and organized as a complete simulation model. Also, an overall power controller with Maximum Power Point Control (MPPT) is proposed to achieve both high-efficiency for solar energy harvesting and grid-connection stability. Finally, simulation results demonstrate the effectiveness of the PV system model and the proposed controller, and power quality issues are discussed.

PACS: 88.05.Ec; 84.30.Jc; 88.05.Gh

## 1 Introduction

Different from stand-alone Photo-voltaic (PV) systems, grid-connected PV systems are connected to and feed generated electricy into utility grids. A grid-connected PV system consists of solar panels, one or several inverters, a power conditioning unit and grid connection equipment [5]. The grid-connected systems rarely include an integrated battery solution. With technology innovation and global penetration of PV power systems over the past decades, PV systems cost has decreased a lot with time, and became more and more acceptable for household power supply applications. Generally, the capacity of home-based grid-connected PV power system is less than 10 kW, and it can meet the load demand of most consumers [9]. The grid-on PV systems can feed excess power to the grid where it is consumed by other users. Some countries such as Germany, China, and some states in USA have issued grid codes and polices to promote individual PV systems grid connection, and also proposed corresponding technical standards to regulate the safety of renewable energy sources and the stability of the main power grid [3, 6, 12, 15]. Moreover, some Middle-East countries such as Qatar has exclusive advantages to develop home-based PV systems because this area has strong sunlight over a long-time period, and most residential compounds are made up of low-height buildings with large sun-facing spaces on the ground and roof. So, it makes a lot of sense to study on significant scientific problems of home-based grid-connected PV systems in such areas. More importantly, an overall high-fidelity simulation model is generally a basis for all technical studies of PV power systems.

At present, some work has been done on the simulation tools/systems for PV power systems. Typical simulation/validation approaches for PV power systems can be classified as mathematical simulations, real-time simulations, Rapid Control Prototype (RCP), Hardware-In-Loop simulations and real-world hardware simulation. Several renowned simulation companies such as dSPACE, Opal-RT, and RTDS have their products and solutions to support simulations of smart-grid or renewable energy generations[1, 16, 17]. Also, some leading IC companies such as Texas Instrument (TI), National Instrument (NI) and ST Microelectronics, and Micro-Chip have also presented their hardware solution and development kits for renewable energy and applications. All these products and solutions provide good support for customized PV system simulation, modeling and prototype development.

Some works focus on specified PV system modeling. [13] studied on an 18 kW level PV system and presented a model and simulation for this system. However, it is an off-grid PV system. A 10 kW PV system is presented in [14], but the system is only for a single-phase grid-tied PV system. [4] focuses on building a 100 kW level three-phase grid-tied PV system, the simulation model is a mathematical model, in which the converters are simplified, and it cannot support high-fidelity dynamics analysis for converters. [7] proposed a simulation model for 100 kW level three-phase grid-tied PV system, but it is only suitable for solar farm analysis due to its power capacity.

Motivated by special demand for home-based three-phase grid-connected PV system simulation, an 8 kW three-phase grid-connected PV system model is presented and studied. In this model, main PV system components such as solar panels, DC-DC converters, DC-AC inverters and three-phase utility grid are modeled based on their physics principle but not mathematically. Also, the overall controller with MPPT is designed and integrated with the converter and inverter modules. Unlike former simulation models, this model not only supports high-fidelity analysis for a home-based PV system but is also suitable for controller validation and hardware-in-loop simulation, because the module is modeled based on the physics and dynamics.

This paper is organized as follows. In Section 2, problem formulation and model structure are presented. The PV array and other key component modules are introduced in Section 3. The overall grid-connected inverter controller is proposed in Section 4. Section 5 is devoted to the presentation of the simulation results. Finally, the simulation results are concluded in Section 6.

## 2.1 Problem formulation

Without loss of generality, an 8 kW three-phase grid-connected PV system model is considered for home-based PV grid integration analysis. In this regard, there are several issues which need to be discussed. Firstly, the structure of the PV integration with grid need to be defined depending on required model accuracy levels. Secondly, the key component - P-Q power controllers needs to be designed and analyzed for the power factor control requirement. Thirdly, a simulation model in the d-q reference frame is essential for the convenience of controller design. Finally, some key model parameters need to be analyzed and tuned based on the simulation result.

## 2.2 Model structure overview

Considering some typical three-phase grid-connected PV systems[8, 10, 11], the proposed 8 kW grid-connected PV system is designed to include four parts: DC part (including PV cells and Boost converters), three-phase inverters, LC filters, and isolation AC transformer. The DC part has capabilities of harvesting electricity from solar energy and Maximum Power Point Tracking (MPPT), which is the same as a single-phase PV system. The three-phase inverters and LC filters are used to convert high-voltage DC power into required three-phase AC power which fit in some grid-connection standard. Finally, the AC power is injected through the isolation transformer into the common access point of the low-voltage power grid.

## 3 Main Component Models

An electrical circuit schematic of the 8 kW grid-connected PV system model is shown in Fig. 1. From Fig. 1 we can see that the PV cells, three-phase inverter, LC filter, isolation transformer, load and utility grid are physically connected. In this section, model and parameters design for main parts including the DC part, three-phase inverter, LC filter, and isolation transformer are presented and discussed.

Figure 1

electrical circuit schematic of the 8-kW grid-connected PV system model.

## 3.1 DC part

The DC part mainly includes PV cell models and a boost DC-DC converter model(marked in orange shown in Fig. 2) in which a Perturb and Observing (P&O) MPPT control algorithm is embedded. As shown in Fig. 2, the input variables of the PV model module are irradiance and ambient temperature, while the output of the PV model module is a voltage signal. Because voltage signals are different from physical voltages in the physics-based PowerSim simulation environment, a voltage-controlled power source is added to convert the PV output voltage signal as a physical output voltage. In the orange-marked part of Fig. 2, a DC-DC boosting topology comprised of capacitors, inductors, IGBT/diode, and Diodes, is designed. Moreover, the boost converter can boost the DC output voltage (Vmpp = 576 V) of the PV array to 620 V DC. Without loss of generalities, a P&O MPPT algorithm is utilized to track the maximum power point of a PV panel energy harvesting. The detailed P&O algorithm flowchart with power converters is shown in Fig. 3 [2]. As can be seen from the flowchart, the MPPT controller can change the PV array output voltage/current based on a maximum power searching strategy. By comparing the generated power Pk at the current instant with previously generated power Pk−1 at last instant, the voltage/current is decreased or increased in one step per time until the peak power point is located. The parameters of the main components in this boost converter topology are listed as below.

Figure 2

DC part including PV cell model and boost MPPT.

Figure 3

P&O algorithm flowchart[2].

1. DC filtering capacitance: 1500 μF;

2. DC boosting inductance: 1 mH;

3. DC-bus capacitance: 3000 μF;

4. Switch: IGBT/Diode.

## 3.2 Three-phase inverter

The three-phase inverter is utilized to convert the voltage from DC to three-phase AC. Also, the Phase Lock Loop (PLL) module inside is used to measure the main grid phase and control the PWM input for the inverter. The main configuration parameters of the three-phase inverter are listed as below.

1. Module name: Universal bridge;

2. Number of bridge arms: 3;

3. Switch: IGBT/Diode.

## 3.3 LC filter

The LC filter is utilized in filtering the original PWM signal from the inverter’s output and improving power quality of the inverter power output. The configuration of the AC-side filtering capacitance and inductance depends on the cut-off frequency of the LC filter. This should be far less than the frequency of the lowest-order harmonic in the inverter PWM output voltage. The main parameters of the LC filtering circuit are listed as below.

1. AC-side filtering Capacitance: 50 μF;

2. AC-side filtering Inductance: 5 mH;

3. Internal resistance:0.1 Ω.

## 3.4 Three-phase Isolation transformer

Isolation transformers provide isolation and are used to protect against electric failure, to suppress electrical noise in sensitive devices, or to transfer power between two circuits which must not be directly connected. Isolation transformers block transmission of the DC component in signals, but allow AC components in signals to pass. There are four configurations to install the isolation transformer, which include Delta to Delta (- use: industrial applications), Delta to Wye, Wye to Delta, Wye to Wye. The delta to Wye is configured in the proposed three-phase isolation transformer model because it is very typical in distributed renewable power systems.

## 4 Three-phase grid-connected inverter controller model

Because distributed renewable energy generators such as PV and wind turbines are sensitive to ambient factors such as irradiance, wind speed, and other weather factors, their output power value is non-constant and discontinuous. Thus, the primary objective of these renewables is to maximize their power harvesting. Therefore, a general solution for a renewable power control is PQ control, which tracks the reference currents by controlling the active power current and reactive power current.

If the output phase voltage of the grid-tied inverter is denoted as u(also grid voltage), and Um is denoted as magnitude of the phase voltage, we obtain: $uaubuc=Umcos⁡(ωt)Umcos⁡(ωt−2π3)Umcos⁡(ωt+2π3)$(4.1)

The d-q transformation (or named as Park transformation) is defined as: $Tabc→dq=cos⁡ωtcos⁡(ωt−2π3)cos⁡(ωt+2π3)−sin⁡ωt−sin⁡(ωt−2π3)−sin⁡(ωt+2π3)$(4.2)

Converting with the d-q transformation, provides: $uduq=Tabc→dquaubuc=Um0$(4.3)

As can be seen from (4.3), the two elements in the d-q reference frame are not coupled. And ud is a constant, while uq = 0.

Define the 3-phased inverter output current as i, the d-axis component and q-axis component by d-q transformation is id and iq individually. Because uq = 0: $idref=Pref/udiqref=−Qref/ud$(4.4)

As can be inferred from (4.4), the reference active and reactive power actually can be tracked by tracking the reference iref. Moreover, the active power depends on id (active power current) and the reactive power depends on iq (reactive power current). Without loss of generality, the PV power system only generates active power (Inverter Power factor is set as 1) and the reference active power tracks the maximum power point of PV panels.

Based on statements above, a sinusoidal PWM(SPWM) based PQ controller is designed for the proposed PV simulation model, which is shown in Fig. 4. As can be seen from Fig. 4, the PQ control module takes the PV panels’ active power output as reference power command, and then converts it into a d-q coordinate current command and input into the current control module. The Sensing and Phase Lock Loop module (SPLL) is utilized to track the grid voltage phase angle and convert the grid voltage and the inductor current in the d-q frame. Moreover, then the current control module takes all the output variables both from the PQ control and the SPLL as the input. Further, it converts the corresponding PWM signal to a three-phase AC waveform.

Figure 4

inverter Controller model structure

## 4.1 SPLL module

The role of the SPLL is to estimate the angle from grid three-phase voltage. By measuring the instantaneous grid three-phase voltage waveforms. Assuming estimation of SPLL as θ and the actual angle is ω *t, the three-phase transform from ABC frame to DQ0 frame can be written as follows: $vdvqv0=23cos⁡(θ)sin⁡(θ)0−sin⁡(θ)cos⁡(θ)0001×cos⁡(ωt)sin⁡(ωt)0V=23cos⁡(ωt−θ)sin⁡(ωt−θ)0$(4.5)

If the SPLL angle is close to the actual grid voltage vector angle, it holds as follows: $ω∗t−θ≈0sin⁡(ω∗t−θ)≈ω∗t−θ$(4.6)

So, based on the approximation above, it can be concluded that the q-axis component in the rotation frame is linearly proportional to the error if the SPLL is locked, which can be denoted as following. $vq∝k(ωt−θ)$(4.7)

Base on the theoretical derivation above, a schematic diagram of SPLL is shown in Fig. 5. SPLL uses a Low Pass Filter/PI to eliminate steady error and a Voltage Controlled Oscillator (VCO) to generate the angle and sine values, so that the grid voltage phase can be locked by a close-loop feedback control.

Figure 5

SPLL schematic diagram.

A detailed model structure of the SPLL module can be seen as Fig. 6. In the SPLL module, a PID controller is employed to track the grid frequency 50Hz. Also, to dispense the affect from the error noise, a low-pass filter is introduced to improve the converted q-axis grid voltage.

Figure 6

SPLL module structure.

## 4.2 Current controller module

The current controller is employed to control static error between the actual current iL and the reference current iLref from the PQ controller. The mathematical model of a grid-tied inverter in d-q reference frame can be denoted as follows. $uduq=LS+rωL−ωLLS+riLdiLq+vdvq$(4.8)

As can be seen from (4.8), the mathematical model is a coupled system, which means that control of the variables is related. So, it is needed to introduce feedback (−ωLiLd and −ωLiLq) and feed-forward of grid voltage, so that d-axis and q-axis currents control can be decoupled. Therefore, the current controller equations with PI control can be denoted as follows. $vdvq=uduq−(kp+kiS)iLdref−iLdiLqref−iLq−−ωLωLiLqiLd$(4.9)

With reference to the mathematical representation shown in (4.9), a detailed structure of the current controller module can be seen in Fig. 7. In the current control module, there are two PID controllers. One PI controller is used to control d-axis current and another PID controller is used to control q-axis current. The two current control is decoupled by adding the feed-forward and feedback terms, and finally the command dq voltage is converted as PWM control.

Figure 7

Current controller module structure.

## 4.3 PQ controller module

The PQ controller module is used to control the active power(P) and reactive power(Q) output from the inverter. Because P and Q satisfy P/Q = tan (θ) and they are coupled, it can also be termed as the power factor θ control. The equation for active and reactive power in the d-q frame can be written as follows: $P=udid+uqQ=uqid−udiq$(4.10)

because uq = 0 as mentioned previously, we can get a mathematical representation for the PQ controller as (4.4).

A detailed structure of the PQ controller module can be seen as Fig. 8. In this module, active power P and reactive power Q is decoupled for control and the reactive power Q can be controlled in two modes: one is to set the Q directly, the second is to set the power factor θ.

Figure 8

PQ controller module structure.

## 5 Simulation Results

In this section, an overall simulation in the Matlab Simulink Environment is designed, and the proposed three-phase grid-connected PV system model and configuration parameters are validated. The PV panels parameters are listed as follows. $Vmpp=576 VImpp=14.2 A$(5.1)

To validate the effectiveness of DC part models, the key variables of the DC part, which include PV array output voltage Vpv, PV array output Current Ipv, duty ratio dutyratio, and boosted output voltageVDC, Simulation results of these variables are shown in Fig. 9. As can be seen from Fig. 9.(a) and (b), the curves of Vpv and Ipv indicate that the boost converter can track the MPP of the PV panels under the MPPT control of P&O algorithm. The MPPT process takes around 0.15 second and the output current waveform oscillate in a small range due to the impact of the boost converter. From Fig. 9.(c) and (d), we can see that the curves of the duty ratio and the DC bus voltage indicate the duty ratio command also oscillate within a small range and the converter output voltage arrives at the right value 620 V.

Figure 9

key variables in DC part.

To our best knowledge, 5-10 kW level PV capacity is typical and reasonable for household PV installations due to cost and area size limits. The PV array is set to generate only active power without reactive power to powering the household power consumptions. In this case, the reference active power is set as 8 kW and the reference reactive power is set as 0 kW. The model simulation results of active and reactive power outputs are shown in Fig. 10. As can be seen from Fig. 10, the generated active power and reactive power into the grid can track closely with the reference real and reactive power.

Figure 10

reference Power Tracking Result.

To validate the effectiveness of the boost converter model, the comparison of active power between the boost converter output and the PV output is shown in Fig. 11. Fig. 11 depicts that both the boost converter power output and inverter power output can closely track the 8-kW reference active power although there is some disturbance during the tracking process.

Figure 11

power output comparison among reference, MPPT and inverter output.

For validating the effectiveness of the grid inverter SPLL module’s performance of grid synchronization, some key variables including phase voltage, phase current, inductor current are selected for comparison of phase synchronization. As can be seen from Fig. 12, the grid voltage, and inductor current are well synchronized, which means the inverter output can track the grid frequency and phase under the inverter PQ control. Because 8-kW active power is set to feed into the grid, there is a small phase error between the output current and inductor current, which means that active power is exchanged between the PV source and the utility grid.

Figure 12

three-phase inverter grid-connection result.

For grid-tied renewable power generation applications, power quality is a key factor which is considered when generated power is injected into the utility grid because power quality could be affected and polluted by harmonics generated from inverters. To evaluate the power quality of the PV system generated power, the indicator -THD (Total Harmonics Distortion) is presented in Fig. 13. As can be seen from Fig. 13, the THD in the inverter output voltage can decrease within around 5/100 under the inverter control, which means it is acceptable for grid connection.

Figure 13

power quality indicator-THD.

based on the above simulation results, we can conclude that this 8 kW model is effective and both the MPPT controller and inverter PQ power controller work well. However, the component parameters of analog parts such as capacitance and inductance in the boost converter and three-phase inverters have an obvious impact on the power control performance. Also, the phase tracking accuracy of the SPLL also plays a key role in the inverter grid connection response speed and power quality. Although the PQ controller presented in this model cannot achieve a better performance and obtain a lower THD value, its structure is simple and easy to improve in future work.

Regarding simulation accuracy, model simulation accuracy depends on many factors such as model structure hierarchy level, model structure accuracy, model measurement accuracy, model identification and calibration parameter accuracy, simulator algorithms metrics, simulation models and so on. Therefore, there are many factors which affected the model and simulation accuracy. However, the model structure hierarchy is a basis and plays a dominant role in the simulation accuracy. Unlike some simplified mathematical models which only focus on controller algorithm, the proposed model in our paper is built based on and the same as the physical hierarchy of PV power system structures, hence the model is considered as a high-fidelity model.

## 6 Conclusion

Aimed at home-based solar PV applications, an 8 kW three-phase grid-connected PV power system model is presented, and the power control issues are studied in this paper. In this model, main components such as PV panels, a boost converter, inverter and utility grid are physically modeling for high-fidelity simulation. Also, a PQ controller is presented and studied for grid-connection control. Simulation results demonstrate the effectiveness of this model and the controllers. Next work will focus on improving and downloading this model into a real-time hardware-in-loop simulation environment such as OPRT eMEGAsim for real-world validation.

## Acknowledgement

The author would like to thank Drs. Said Mansour and Antonio P. Sanfilippo for their support on the research work on PV grid integration.

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Accepted: 2017-05-25

Published Online: 2017-09-26

Citation Information: Open Physics, Volume 15, Issue 1, Pages 603–612, ISSN (Online) 2391-5471,

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