Voltage and Frequency controller for parallel Inverters in Microgrid using Fuzzy logic

Abstract

The inverters in Microgrid are connected in parallel to improve efficiency, increase transmission capacity, and easy to repair and maintain. When the Microgrid is operating in standalone mode, the inverters must be controlled to share their power according to the rated ratio, this is to stabilize the frequency and voltage in the Microgrid. The droop control method for power control for parallel-connected inverters is one of the most popular power-sharing methods today, some studies have presented traditional and improved droop control methods. However, the purpose of the studies is power-sharing for the inverters that no purpose of reducing the voltage and frequency deviation to improve power quality. This paper is shown the adjusting of the voltage and frequency method based on fuzzy logic with an aim is minimize the voltage and frequency deviation for improving power quality in Microgrid. This controller consists of a Droop combined with fuzzy logic to control changes in the slope of the power curve when the load changes, thereby the voltage and frequency deviation could be adjusted. This control method is called the Droop-fuzzy logic control method. Experimental results confirm the validity of the proposed control. Simulation and experimental results will prove the effectiveness of the proposed method.

Introduction

Distributed energy sources such as wind energy, solar energy,... they are sent through power converters. There are many different types of microgrid configurations, usually microgrids need an inverter to create AC voltage, the AC voltage at the inverter output is supplied to AC loads or connected to the grid.. Power transmission in microgrid achieves high efficiency when inverters are connected in parallel 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 .

However, in stand-alone mode, the microgrid must have power sharing between inverters connected in parallel to maintain voltage and frequency stability. At the same time, this power sharing will help avoid balancing currents flowing between inverters 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 .

Based on the power characteristics of the source, previous studies have established a mathematical model for the droop controller to control the power-sharing between inverters operating in parallel. The droop controller controls active power according to frequency and controls reactive power according to voltage. Relationship between active power and frequency; Reactive power and voltage are expressed through slope coefficients 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 . Therefore, researchers relied on the slope factor to realize power sharing between parallel-connected inverters. However, previous studies often fixed these slope coefficients 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , so when load parameters change a lot, the resulting voltage and frequency at the output of the inverters given by this droop controller will have a much larger deviation from the rated value.

Several studies have presented traditional droop control methods for power sharing. The purpose of this study is to share power among inverters without aiming to reduce voltage and frequency deviation to improve power quality. However, the traditional droop controller is affected by the line impedance parameter. Therefore, there have been several studies presenting improved droop control methods 10 , 11 , 12 , 13 , 14 , 15 for power sharing. However, the purpose of these studies is to improve the accuracy of power-sharing for inverters without aiming to reduce voltage and frequency deviations to improve power quality.

Therefore, this paper designs a droop controller combined with fuzzy logic to overcome the disadvantages of previous controllers.

The contributions of the proposed controller are described below:

The droop-fuzzy logic controller automatically adjusts the slope of the droop characteristic curves when the load changes. Therefore, this controller will minimize the frequency and voltage deviation, it improves power quality in microgrid.

In addition, the droop-fuzzy logic controller correctly power-sharing between the parallel-connected inverters in the Microgrid.

Typically, the structure of an islanded microgrid consisting of inverters operating in parallel is shown in Figure 1 . In standalone mode, the microgrid must be capable of self-stabilizing voltage and the frequency under load conditions changes in real-time.

Figure 1 . Common structure of an independent microgrid

Typically, the traditional power control scheme of an independent microgrid includes two control loops:

• The outer control loop is the power control loop. Previous studies often used a droop controller for this control loop, because the droop controller is easy to use, does not require communication, and is easy to change. However, the droop controller will give incorrect power division results in the case of different line impedances, or different inverters. Therefore, in this article, we propose a method to improve the droop controller by using fuzzy logic.

• The internal control loop is a voltage control loop and a current control loop. This control loop will control the voltage and current at the output of the inverter according to the reference voltage and current values.

The block diagram of the proposed controller is shown in Figure 2 .

Figure 2 . Block diagram of the proposed controller for an inverter in islanded microgrid

METHOD

Theoretical basis of the proposed control method

The traditional droop controller for dividing power between inverters is established based on the equivalent circuit of the inverter connected to the load through a line as shown in Figure 3 .

Figure 3 . The equivalent circuit of the inverter connects to the load through the line

According to research 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , the power running on the line is calculated according to the expression as Eq. 1 ( Figure 23 ):

In there:

R(Ω) and X(Ω) are impedance parameters of the line.

V(voltage) is the voltage at the beginning of the line.

P(W) and Q(Var) are the powers running on the line.

V _PCC (voltage) is the voltage at the PCC.

δ is the phase difference angle of the voltage V anh V _PCC : δ = δ ₁ - δ ₂

Transforming expression (1), we have: Eq. (2) and Eq. (3) ( Figure 23 )

The actual angle between the output voltage of inverters and PCC bus voltage δ is a small value, so sinδ ≈ δ and cosδ = 1, X>>R, from equation (2) and (3) we have: Eq. (4) and Eq. (5) ( Figure 23 )

Equations (4) show that: P depends on frequency f. From there, we can establish P/f droop controller to control the active power of the inverters as Eq. 6 ( Figure 23 ):

The droop graph of equation (6) is drawn in Figure 4 .

Figure 4 shows that when the power P changes, the frequency f also changes. If the load increases significantly, the frequency will decrease significantly compared to the rated value and vice versa.

Figure 4 . Droop P/f plot

Equations (5) show that: Q depends on voltage V. From there, we can establish Q/V droop controller to control the reactive power of the inverters as Eq. (7) ( Figure 23 ):

The droop graph of equation (7) is drawn in Figure 5 .

Figure 5 . Droop Q/V plot

Figure 5 shows that when the power Q changes, the voltage V also changes. If the load increases significantly, the voltage will decrease significantly compared to the rated value and vice versa.

Where:

V ₀ is the nominal amplitude voltage.

f ₀ is the nominal frequency.

V is the measured amplitude voltage of the inverter.

f is the measured frequency of the inverter.

P ₀ is the nominal active power of the inverter.

Q ₀ is the nominal reactive power of the inverter.

m _p and m _q are the droop coefficients, which are calculated as Eq. (8) ( Figure 23 ):

Design of the fuzzy logic controller

Figure 4 and Figure 5 show that when the power consumption of the load changes, the frequency and voltage also change. If the load increases significantly, the frequency and voltage will decrease significantly compared to the rated value and vice versa. Dividing the power to the inverters according to the rated ratio is done by expression (8). We see that expression (8) has a constant value for each inverter, so the slopes of the P/f and Q/V droop curves do not change during operation. In fact, the load always changes in real time, which will lead to a situation where the voltage and frequency of the microgrid deviate too much from the rated value. This is also something we do not want. Therefore, this article provides a method to change the slope of the drop graph using fuzzy logic.

Equations (6), (7) and Figure 4 , Figure 5 show that: a change in the active power of the consumed load (∆P) will cause a corresponding change in frequency (∆f). Similarly, a change in the reactive power of the consuming load (∆Q) will cause a corresponding change in voltage (∆V). If these changes are significant, it will create unsatisfactory voltage quality in the microgrid. It may also cause balanced currents to flow in the inverters, which will cause damage to the inverters.

V=V ₀ and f=f ₀ can only be obtained when Q=Q ₀ and P=P ₀ .

The equations (6) and (7) show that the power-sharing for inverters depends on the slope coefficients determined in equation (8). Figure 4 , Figure 5 shows that the frequency at the output of the inverter changes according to the active power of the load and the voltage at the output of the inverter changes according to the reactive power of the load; The graph of droop P/f and Q/V in (6) and (7) have slopes that depend on (8). When the slopes (8) change, the power sharing will change accordingly. Therefore, this paper proposes a method to shift the slope coefficients m _p and m _q according to changes in the load instead of fixing them according to the equation (8).

In the conventional droop method, the slope coefficients m _p and m _q are fixed according to equation (8). When the load increases or decreases sharply, the frequency and voltage at the output of the inverter will deviate much from the value of its norm. In the proposed method, the slope coefficients m _p and m _q are adjusted to change according to the load. When the load increases or decreases sharply, the frequency and voltage at the output of the inverter will deviate less than with the conventional droop method.

The slopes m _p and m _q of the P/f and Q/V curves are varied by the fuzzy controller. The block diagram for the proposed droop-fuzzy logic controller is shown in Figure 5 . Figure 6 is combined from equations (6), (7) and fuzzy-logic block to adjust the slope coefficients m _p and m _q . Whereas the conventional droop controller is implemented according to equations (6) and (7), m _p and m _q are fixed according to formula (8) as the Figure 7 . Therefore, the conventional droop controller will give control results with larger voltage and frequency deviation than the proposed method.

Figure 6 . The proposed controller

Figure 7 . The conventional controller

Design of fuzzy controller to adjust mp slope:

This fuzzy controller has two inputs and one output :

The first input is the difference between the actual value and the rated value of the active power: e _p = P – P ₀

The second input is the rate of change of active power over time: dP/dt

The output of this controller is the slip coefficient m _p .

Select language variable for input signal:

Language variable for e _p input:

NB: more negative; NS: less negative; ZE: equal zero; PS: less positive; PB: much positive

Language variable for dP/dt input:

N: negative; Z: zero; P: positive

We can choose more language variables for input and output for better tuning.

Select value domain for input signal:

Depending on the change of actual load capacity compared to the rated capacity value, we choose the appropriate value range.

Select value domain for e _p input: [-1000 1000]

Depending on the rate of increase or decrease of the actual load capacity, we choose the appropriate value range.

Select value domain for dP/dt input: [-100 1000]

Based on the sliding coefficient calculation expression (8), we choose the value range for the m _p output. Usually the m _p value is very small, so we choose many language variables for the output to make the adjustment more accurate.

Select value domain for m output: [0; 5.e ^-4 ]

Language variable for m output:

A1, A2, A3: small; B1, B2, B3: medium; C1, C2, C3: big

Choose membership functions for the inputs:

We can choose a membership function of triangular or trapezoidal shape for the input as shown in Figure 8 , Figure 9 . We can choose a bar-shaped membership function for the output as shown in Figure 10 .

Figure 8 . Membership function of input e _p

Figure 9 . Membership function of input dP/dt

Choose membership functions for the output :

We can choose a membership function that is triangular, trapezoidal, or linear.

Figure 10 . Membership function of output m _p

Design of fuzzy controller to adjust m

This fuzzy controller has two inputs and one output :

The first input is the difference between the actual value and the rated value of the reactive power: e _q = Q – Q ₀

The second input is the rate of change of reactive power over time: dQ/dt

The output of this controller is the slip coefficient m _q .

Select language variable for input signal:

Language variable for e _q input:

NB: more negative; NS: less negative; ZE: equal zero; PS: less positive; PB: much positive

Language variable for dQ/dt input:

N: negative; Z: zero; P: positive

We can choose more language variables for input and output for better tuning.

Select value domain for input signal:

Depending on the change of actual load capacity compared to the rated capacity value, we choose the appropriate value range.

Select value domain for e _q input: [-1000 1000]

Depending on the rate of increase or decrease of the actual load capacity, we choose the appropriate value range.

Select value domain for dQ/dt input: [-1000 1000]

Depending on the rate of increase or decrease of the actual load capacity, we choose the appropriate value range.

Select value domain for dQ/dt input: [-100 1000]

Based on the sliding coefficient calculation expression (8), we choose the value range for the m _q output. Usually the m _p value is very small, so we choose many language variables for the output to make the adjustment more accurate.

Select value domain for m output: [0; 5.e ^-4 ]

Language variable for m output:

A1, A2, A3: small; B1, B2, B3: medium; C1, C2, C3: big

Choose membership functions for the inputs:

We can choose a membership function of triangular or trapezoidal shape for the input as shown in Figure 11 and Figure 12 . We can choose a bar-shaped membership function for the output as shown in Figure 13 .

Figure 11 . Membership function of input e _q

Figure 12 . Membership function of input dQ/dt

Choose membership functions for the output :

We can choose a membership function that is triangular, trapezoidal, or linear.

Figure 13 . Membership function of output m _q

Define control rules:

Equations (6), (7), (8) and Figure 4 , Figure 5 show them:

If Q > Q ₀ then V < V­ _0, In order for V to get close to V ₀ , we have to control to decrease the slope mq, which means we have to control to increase the angle α.

If Q < Q ₀ then V > V­ _0, In order for V to get close to V ₀ , we have to control to decrease the slope mq, which means we have to control to increase the angle α.

If P > P ₀ then f < f­ _0, In order for f to get close to f ₀ , we have to control to decrease the slope mp, which means we have to control to increase the angle α.

If P < P ₀ then f > f _0, In order for f to get close to f ₀ , we have to control to decrease the slope mp, which means we have to control to increase the angle α.

On the other hand, we rely on the language variables, the range of values, the membership function of the input and the output, we can set up the control rules as shown in Table 1 .

If e _p = NB (P <

0 ) and = N (P is decreasing) then we choose m _p output as A1.

If e _p = NS (P <

0 ) and = N (P is decreasing) then we choose m _p output as B1.

If e _p = ZE (P =P ₀ ) and = N (P is decreasing) then we choose m _p output as C1.

If e _p = PS and dP/dt = N then we choose m _p output as B3.

If e _p = BP and dP/dt = N then we choose m _p output as A3.

If e _p = NB and dP/dt = Z then we choose m _p output as A2.

If e _p = NB and dP/dt = P then we choose m _p output as A3.

If e _p = NS and dP/dt = Z then we choose m _p output as B2.

If e _p = ZE and dP/dt = Z then we choose m _p output as C2.

If e _p = PS and dP/dt = Z then we choose m _p output as B2.

If e _p = PB and dP/dt = Z then we choose m _p output as A2.

If e _p = NS and dP/dt = P then we choose m _p output as B3.

If e _p = ZE and dP/dt = P then we choose m _p output as C3.

If e _p = PS and dP/dt = P then we choose m _p output as B1.

If e _p = PB and dP/dt = P then we choose m _p output as A1.

Similarly, we can choose the control law for the fuzzy controller m _q

Choose the composition rule according to the Sum-Prod principle. Defuzzification by the centroid method.

Calculation and low-pass filter

The instantaneous power p and q are calculated according to the instantaneous value of the current flowing on the line (i ₂ ) and the voltage at the beginning of the line (v _c ) in a stationary dq0 frame as Eq. (9) and (10) ( Figure 23 ):

The current controller and voltage controller

Based on the equivalent circuit shown in Figure 14 , we set up these controllers.

Figure 14 . Equivalent schematic of inverters connected to a load.

Where:

R (Ω) and L (H) are resistor and inductance of the line.

R _f (Ω) and L _f (H) are resistor and inductance of the filter (H).

Applying Kirchhoff's laws to the circuit of Figure 14 , we have the following equations (11) and (12) ( Figure 23 ):

Projecting equation (12) onto the coordinate system dq0. The voltage bias is eliminated by the PI controller on both the d-axis and the q-axis, the d-axis voltage bias is added with a feedback component (-ωCv _cq ), and a voltage bias on the q-axis is added feedback component(ωCv _cd ). According to [15], the capacitance of the filter capacitor is usually very small, so the C dv _cd /dt and C dv _cq /dt components are ignored, the equations (11) can be written as Equation (13) and (14) ( Figure 23 ).

Equations (13) and (14) are the voltage controller.

Projecting equation (12) onto the coordinate system dq0. The current bias is eliminated by the PI controller on both the d-axis and the q-axis, the d-axis current bias is added with a feedback component (-ωL _f i _1q ), and a current bias on the q-axis is added feedback component (ωL _f i _1d ). According to [15], the inductance and resistance of the filter capacitor is usually very small, so the (L _f (di _1d )/dt + R _f i _1d ) and (L _f (di _1q )/dt + R _f i _1q ) components are ignored, the equations (12) can be written as equation (15) and (16) ( Figure 23 ):

Equations (15) and (16) are the current controller.

SIMULATION RESULT AND DISCUSSION

Simulate power control for a microgrid consisting of three inverters connected in parallel using Matlab/simulink software. Simulations are performed by the conventional controller and the proposed controller to compare the results. Simulation parameters are given in Table 1 .

Table 1 SIMULATION PARAMETERS

Case 1:

Power sharing simulation for two inverters in an independent microgrid is performed using the proposed controller.

Figure 15 . The graph showing the change of slip coefficients (mp, mq) and frequency and voltage as the load increases

Figure 16 . The waveform of voltage and current at the load

Figure 17 . Output power of two inverters

Figure 15 a and 15b show that for an erroneous value of active power (e _p ) at the input of the fuzzy logic block, there will be a corresponding slope coefficient m _p at the output of the fuzzy logic block. The value of m _p is within the specified range selected (the range of values is selected by formulas (6), (7), and (8)). On the other hand, when the e _p deviation decreases, m _p increases (increases in the selected value range), and vice versa when the e _p deviation increases (from 6s onwards) the m _p decreases. These results are completely consistent with the fuzzy control law established. Figure 15 c shows that when the slope coefficient m _p changes, the frequency at the output of the Droop-fuzzy logic controller or the output frequency of the inverter also changes accordingly, the curve of frequency shows as the load increases then the frequency decreases, which is also completely consistent with the equation (6) and power curve in the Figure 4 . The f value is also calculated according to m _p and e _p in equations (7), (8), and the frequency deviation from the norm is calculated in Table 2 . Table 2 shows that the frequency deviation is very small, this result is due to the fuzzy-logic controller that controls to change m _p when the load changes. As we see in the Figure 4 , if we don't change the slope of the droop curve P/f as the load changes, then a power deviation ∆P will give a corresponding frequency deviation ∆f, and when the load changes more, then the ∆f will be large. Same as above, Figures 15d and 15e show that for a deviation of reactive power e _q , it will give a value of slope coefficient m _q in the selected range of values, and we see that when the deviation e _q decreases, the slope coefficient m _q increases and vice versa, at t=6s, the e _q deviation continues to decrease compared to the previous one, so the slope coefficient m _q at continues to increase. This is completely consistent with the fuzzy control law established. Figure 15 f shows that when the slope coefficient m _q changes, the voltage at the output of the Droop-fuzzy logic controller or the output voltage of the inverter also changes accordingly, which is also completely consistent with equation (7) and power curve in Figure 4 b. The voltage value is also calculated according to m _q and e _q in formula (7), (8), voltage deviation from the norm is calculated in Table 2 . Table 2 shows that the voltage difference is very small, to get this result is because we control the slope of the power characteristic curve when the load changes. As we see in Figure 5 , if we do not change the slope of the power curve Q/V when the load changes, then a power deviation ∆Q will give a corresponding voltage deviation ∆V, and when the load changes more, then the∆V will be large.

Table 2 Table of results for frequency and voltage deviation from rated value

Figure 16 , Figure 17 show the Droop-fuzzy logic control method for a good dynamic response as soon as the load changes and the current and voltage stabilizes well right after the load changes. The output power of the inverters is divided exactly in a 1:1 ratio.

The simulation results above show that the proposed method controls the correct sharing power for the inverters and reduces the voltage and frequency deviation when the load changes suddenly, improving the quality of the power supply for the load, and a good dynamic response. The proposed method has overcome the disadvantages of the conventional or improved droop methods because the slope of this power curve is always fixed, so when the load changes, the voltage and frequency deviations cannot be adjusted to improve power quality.

Case 2:

Two inverters have the same rated power, they are connected in parallel, Simulate power division by the proposed method.

Figure 18 . The graph of sharing active power, reactive power, and voltage at load when simulated by the proposed droop-fuzzy controller

Figure 19 . The graph of sharing active power, reactive power, and voltage at load when simulated by the conventional droop

Figure 18 shows that the proposed controller gives good power division results, the power division results in the time period from 0s to 5s have the following deviations:

e _p % = (P _i - P ^* _i )/(P ^* _i ).100% = (1118-1110)/(1110).100% = 0.72 %

The error of sharing the reactive power of inverters for the period from 0s to 5s:

e _q % = (Q _i - P ^* _i )/(Q ^* _i ).100% = (625-620)/(620).100% = 0.8 %

This shows that the proposed method gives highly accurate power division results.

Figure 19 shows that the conventional droop controller gives poor power-sharing results, the error is very large when sharing reactive power. The error of sharing the reactive power of inverters for the period from 0s to 5s:

e _q % = (Q _i - P ^* _i )/(Q ^* _i ).100% = (644-620)/(620).100% = 3.8 %

The voltage graph in Figure 18 also shows that the voltage deviation given by the proposed drooping fuzzy controller is very small, especially as the load increases, the voltage drop is smaller than the voltage graph in Figure 19 .

Case 3:

Use the proposed method to divide the power between the two inverters according to the rated power ratio of 2:1, P _dm1 =2P _dm2

Figure 20 . The graph of sharing active power, reactive power, and voltage at load by the proposed droop-fuzzy controller

Figure 20 shows that the proposed controller has given the correct power-sharing results with the rated power ratio 2:1, its transient response and steady-state response are also very good, and the time steady-state set up early.

Case 4:

Use the proposed method to divide the power between the three inverters according to the rated power ratio of 1:1:1, P _dm1 =P _dm2 =P _dm3 .

Figure 21 . The graph of sharing active power, reactive power, and voltage at load by the proposed droop-fuzzy controller

Figure 21 shows that the proposed controller gave the correct power-sharing results with the rated power ratio 1:1:1, its steady-state response is very good, and the time steady-state is set up early.

Case 5:

Use the proposed method to divide the power among the three inverters according to the rated power ratio of 1:1:1, the load varying in this case.

Figure 22 . The graph of sharing active power, reactive power, and voltage at load by the proposed droop-fuzzy controller

Figure 22 shows that the proposed controller gave the correct power-sharing results with the rated power ratio even when the load has changed.

The above simulation results show that the proposed controller gives good results, negligible deviation, and relatively early setup time. Good voltage quality, low voltage and frequency deviation.

Figure 23 . Equation

Conclusion

In this paper, a sliding coefficient adjustment method using fuzzy logic is proposed, improving the traditional droop controller. This innovation allows to significantly improve the accuracy of power sharing for inverters in the microgrid, improve the quality of voltage supplied to loads, and reduce frequency deviation. The advantages of the proposed method were verified by simulation for microgrids with two and three inverters.

CONFLICT OF INTEREST

There is no conflict of interest regarding this manuscript.

AUTHOR CONTRIBUTION

Xuan Hoa Thi Pham have writen this entire paper.