The Modified Control Method for the Single-Stage Three-Phase Grid-Connected Photovoltaic System

Single-stage topology and the maximum power point tracking (MPPT) algorithm have advantages such as simple configuration and high efficiency in grid-connected photovoltaic (PV) systems. In conventional systems, current and voltage sensors of PV system are normally used for MPPT. This paper presents a modified control algorithm for the single-stage three-phase grid-connected PV system without PV current sensor with a variable step MPP-tracker. This algorithm is not derived from complex state equations and is not dependent on any circuit parameters. It simply calculates the output power of the inverter to replace the input power of the PV systems in the MPPT algorithm. The modified algorithm is simulated by using Matlab/Simulink software and implemented in the experimental prototype. With the single-stage configuration and PV current sensorless method, the prototype is suitable for lowcost high efficient implementation in the practice.


INTRODUCTION
Nowadays, PV energy system is one of important source for sustainable development in most of countries all over the world.It features pure source and easy-to-install system.Moreover, it does not require complex and usual maintenance.Often, there are two categories for photovoltaic (PV) systems: 1) standalone system and 2) direct grid-connected system.Standalone systems are in low-power application and use many battery banks for power reservation.In direct grid-connected application, the PV system power is converted and directly injected into electricity grid.
The PV power and voltage have a non-linear relationship.Therefore, it is indispensable to operate a PV system in maximum power point.

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The maximum power point (MPP) is dependent on environmental elements, such as irradiation, temperature.The maximum power point tracking (MPPT) algorithms are developed for those PV systems always produce the maximum power regardless of the environment.During years, many MPPT methods have been developed and implemented such as Hill Climbing/P&O, Incremental Conductance (IncCond), Fractional Open-Circuit Voltage or Short-Circuit Current methods, based on Fuzzy logic or Neural Network methods [1][2][3][4][5][6][7].
The maximum power point tracker (MPPTer) usually requires two sensors in the input side for PV system voltage and current.However, the PV system voltage, current and grid currents have relation based on mathematical equations.Thus, some strategies are developed to estimate the information of PV system voltage or PV system current without sensors.These algorithms are often affected by circuit parameters or based on complex theory of observer [8], [9].These problems make the algorithms difficult to implement in practice.
The single-stage grid-connected PV systems have been presented in many publications [10][11][12][13][14].In these systems, both current and voltage sensors of PV array are usually used to realize MPPT.In the other work [15], unlike other MPPT methods, only PV array's output voltage is required to be sensed to implement MPPT.However, the algorithm for this scheme is quite complex and suitable only for a single phase grid-connected inverter.
With a goal to minimize the cost and control complexity, this paper presents a low-cost singlestage three-phase grid-connected PV system without the PV array's output current sensor.The modified algorithm observes the output power of inverter instead of the input power of PV system.

CONVENTIONAL AND PROPOSED SINGLE-STAGE THREE-PHASE GRID-CONNECTED PV SYSTEM WITH MPPT ALGORITHM
Single-stage configuration is used to remove the DC/DC converter.This configuration is useful to increase the efficiency and decrease overall cost (Fig. 1).Fig. 2 and the equation ( 1) show the relationship between DC-link voltage, inverter and grid voltages.MPPT algorithm for single-stage configuration is based on Udc-controling ability of the inverter.The inverter changes the altitude of Id (d-axis value of grid-current-space-vector in the gridvoltage-coordinate) to change Udc into Udc-reference.MPPTer detects the maximum power point (Vref = VMPP).Afterthat, the inverter will keep the Udc approximately equal to this value as showing in Figure 3a.
Block MPPT: using any MPPT algorithms such as P&O, Incremental Conductance... Receiving PV system voltage and current, this block determines the optimal voltage for operating in next step.The output voltage Vref is kept closer and closer the maximum power voltage.
Block Control: controlling three currents injected into grid.Some methods can be used to control the currents [16], [17]: PI control, hysteresis control (Fig. 3b), deadbeat control...In this paper, the hysteresis algorithm is used because of simplicity and flexibility.Often, Iq_ref is kept zero so that the grid current and the grid phase voltage are in the same phase, unity power factor.Beside that, Iq_ref can be different from zero to compensate the reactive power as desired.

Principle of DC-link Voltage Balance
Active power P and reactive one Q are controlled by tuning the values of Id and Iq of grid currents.Where (Id, Iq) is two components of grid current space vector in the rotation grid voltage coordinate, d-axis is identical with the grid voltage space vector (Fig. 3c).The simultaneous value of (P, Q) injected into grid must ensure the stability of DC-link voltage.As mentioned above, Q is often set to zero, only P is changed to stabilize DC-link voltage (Fig. 4).
In addition, the active power P can be calculated in terms of the Id component: where Vgd is grid voltage and Id is grid current.Thus, control loop can change Id value to keep the DC-link voltage fixed.
_ _ _ _ : : The grid currents presented in this paper have the assigned direction from inverter to grid.

The proposed control algorithm for single stage three-phase PV system
The proposed algorithm uses only voltage sensor of PV array output and the MPPTer has to be detect the MPP (Fig. 5).In the block schema of proposed control algorithm (Fig. 6), the input of MPPT block includes VPV and Id.Due to principle of DC-link voltage control, the input power and the output power will be equal when Udc-link value balances out.Therefore, instead of Pin observation, the MPPT block can observe Pout to track the MPP.In this case, PV current value is unnecessary for MPPT because the MPPT block do not need to know the PV power, so the current sensor for PV array can be removed.The new algorithm will control the PV voltage operation point to attain the maximum value of Id.
At the beginning, the MPPTer will adjust the DC-link voltage (VPV) to be equal to the initial voltage reference (Vref).It may be done by using the fractional open circuit voltage MPPT method, as following: where VOCthe open circuit voltage of PV array When the VPV is steady, the Id value will be observed.If the Id value in this step is bigger than the previous step value, Vref will be changed as same way as the previous step.Otherwise, Vref will be changed as inverse way as the previous step (Fig. 7).Thus, the stable Vref is in the operation point having maximum Id value.
The proposed algorithm is based on the method with variable step change of Vref.Unlike other MPPT methods, the input power is substituted by Id value which is easy to calculate (Fig. 7).In addition, the Id_ref is observed instead of Id because the Id_ref value has a little noise than Id value and relatively identical to Id in steady state.
In case of using fixed step, if the step size is large, the PV operation point will reach to MPP rapidly but oscillate around this point.In opposite way, if the step size is small, the operation point will be steady at the MPP but it takes a long time to reach to this point.To overcome this drawback, the proposed MPPT method uses variable voltage step size as below equation ( 5), the step size depends on the difference of Id(k) and Id(k-1).In this equation, the value of coefficient K is determined by using such as the optimizationbased algorithm.The variable step size can combine two advantages of small step size and large step size; they are fast response time and stable operation point.At the starting, the operation point is far from MPP, the difference (Id(k) -Id(k-1)) is big, so the step size dV is also big to get MPP rapidly.After a short time, the operation point is moved to MPP, the difference (Id(k) -Id(k-1)) is small gradually and is equal to zero when it reaches to MPP, so dV is smaller than the previous one and remains zero at MPP to get the stable operation point.

Model of estimating power loss and efficiency of VSI
Estimating efficiency of solar inverters is usually based on calculating power loss of switching device [20][21][22][23].Calculating the power loss of semiconduting switches is expressed as the following.
When a switch is operating, there are four types of power loss: conducting loss, off-state loss, switching loss, driving loss.Comparing with conducting loss and switching loss, off-state loss and driving loss are so small that they can be neglected.The switching loss depends on the switching energy (EON and EOFF) and switching frequency, the conducting loss depends on voltage (VCEO), resistance (RCEO) and value of current which is through the semiconducting device.The above parameters is provided by the producers, they can be selected appropriately according to operating condition and operating mode.
Energy converting efficiency of VSI is based on estimating the total power loss of semiconducting switches and it is calculated by the following formula: With  is efficiency, Pin is input power of VSI, PLtotal is power loss of semiconducting switches.
The input power of VSI is determined by the formula:

Estimating power loss of IGBT
Power loss of IGBT consists of conducting loss and switching loss, it is calculated by the following formula:

Estimating power loss of Diode
Power loss of a didoe is similar to above, it is calculated by the following formula:

SIMULATIONS OF THE PROPOSED CONTROL METHOD FOR LOW-COST SINGLE STAGE THREE-PHASE PV SYSTEM
Whole simulation model is built in Matlab/Simulink with SimPowerSystem Toolbox (Fig. 8).
The simulation results for the irradiation change case are shown in Fig. 9.
The input power is measured to demonstrate the operation points of PV system easily.In addition, the estimated power can be used to plot and test without measuring input power.The estimation is based on expression (2), where Vgd is grid phase voltage (rms) and Id is in rms (Fig. 10a).
The grid current phase is identical to the grid voltage phase.When the irradiation changes, the magnitude of grid current is decreased (Fig. 10b).
The efficiency of VSI is evaluated by using the estimation block (Fig. 8c), which is based on expressions ( 6)-( 9).The high efficiency of PV inverter is obtained as shown in Fig. 10c, while the irradiation changes from 1 to 0.7 at 0.5s.

PV System
Inverter and L-Filter Grid

EXPERIMENTAL RESULTS
A prototype is used to verify the proposed algorithm.In the experiments, a PV system current sensor is additionally used to measure input power.Similar to simulation, an estimated power is calculated for plotting and checking based on the relationship expression between output power and Id value.
The experimental model (Fig. 11) includes: PV system: 15 panels, Kyocera KC50T, installed in series The Power Analyzer Fluke 43B is utilized to show the power factor, grid current harmonics… The proposed control method is programmed by dSPACE 1103.The user interface (Fig. 12), for controlling and plotting, is built in ControlDesk.
As shown in the Fig. 12, the measuring value and the reference value is relatively equivalent, such as VPV and Id.The estimated power is very close to the input power which determined by sensors.However, the estimated one is not completely steady.It slightly changes around the measured power.The secondary currents mean the current in the inverter side, not in the grid side because of step-up transformer.
The true P-V curve, not estimated, is easier to observe the maximum power point (Fig. 13a).
The algorithm control the secondary current phase to be the same as the grid voltage phase for unity power factor (Fig. 13b).Because the grid voltage and the secondary votage have the same phase, the power which measured in the secondary side has the maximum power factor (Fig. 14a).The quality of output currents is shown in Fig. 14b.The THD is smaller than 5% and can be reduced when the PV system power increases.The magnitude of high order harmonics is much smaller than the basic harmonic (Fig14c).

2-level Inverter
The experimental results demonstrate good responses as shown in above figures.The responses of electrical quantities in low-cost single-stage three-phase PV system are obtained quickly and precisely.

CONCLUSION
This paper presented a modified control method for single-stage three-phase gridconnected PV system, which has the advantages of the high efficiency, cost-effectiveness and simplicity.Unlike other MPPT methods, the input power is substituted by Id value which is easy to calculate.Moreover, the output power, actually Id, is observed to replace the input power.Hence, the PV array output current sensor can be removed.Beside that, the proposed MPPT algorithm is based on the method with variable step change of Vref in order to accelerate the MPPT response.
In this work, the hysteresis current control and L-filter are implemented.Advanced methods of current control, such as PI, deadbeat, and LCLfilter could be considered to improve the quality of grid currents.The DC-link voltage balancing principle has been used.However, other configurations are being researching to apply this new MPPT idea possibly.

Figure 7 .
Figure 7.The flowchart of proposed variable step change of MPPT algorithm 8) With VCEO : on-state zero-current collectoremitter voltage RCEO : collector-emitter on-state resistance EON : turn -on energy EOFF : turn -off energy IC(AV) : average value of collector current IC(RMS): RMS value of collector current VCE_bl: blocking collector-emitter voltage VCE_ref: blocking collector-emitter voltage from