Compound control method for overcoming transmission delay impact on networked control inverter for AC microgrid

Abstract

Recent studies show that power electronic system performance can be improved by combining with communication technologies, however, time-delay impact that is introduced by network could cause performance degradation. As for networked control inverters, such delay results in an increase in the THD of the output. To solve the time-delay impact, in this paper, we propose a wireless network control inverter architecture. It transmits the information of AC microgrid by Zigbee and a compound control method (internal model control and quasi-PR control) of networked control inverter is proposed. The architecture enables remote control of the inverter and wireless parallel connection, the method can either reduce the THD increase and the circumfluence of wireless parallel inverters. The proposed method is concretely applied in networked control system of quasi-PR controlled AC microgrid in grid mode. The simulation and experimental results are presented to prove the proposed control on several operating condition, which provide a competive performance.

Keywords

Network-based control transmission delay compound control method AC microgrid

1 Introduction

In recent years, the penetration rate of new energy in the power grids has grown rapidly. Renewable Energy sources such as wind and solar are characterized by randomness, volatility and wide distribution, and it is difficult to adapt to the operational needs of traditional power grids [14 , 23]. The micro grids can realize a large amount of distributed generator’s local consumption. Therefore, in order to adopted with the traditional power grid, communication technology has become more and more important in the power electronics field [4, 31]. Power electronics systems based on networked control will have greater adaptability, scalability and better performance.

But the time delays caused by network have some negative effects on control systems in power grid. Ghosh explored how to minimize the negative effects of such delays in smart gird [12 , 30]. Inverters play a central role in micro grids. Due to the introduction of the network, there will be problems with transmission delay, which will bring new challenges to the control of the inverter. Many scholars have researched on the problems of inverters caused by delay. Zhang has proposed a suit of analytical method, that both delay-insensitive and delay-sensitive control strategies of network-based system have their different theoretical methods and problem-solving paths [31, 32]. Used in droop-controlled AC microgrid system, and shows some effectiveness. There is delay in a digital controlled system because of the DSP and A/D converters, which is always called control delay. The control delay will result in reduced output performance, Moghaddam analyzed the negative effects of the delay during one sampling period [5], then they proposed a predictive current observer-based controller. For three-level neutral-point-clamped inverters, Zhou find that the delay causes additional NP potential fluctuations, and increases the THD of the output current [26], then a control delay compensation method is proposed. Ghaderi research on the stability issue of three-phase grid-connected inverters [18], they find the delay-power relationship for grid-connected inverters. The relationship is the higher power leads to a lower stability margin. Ghosh proposed two methods in order to minimization of adverse effects of time delay in power grid [21], the fuzzy logic controller and the modified predictor. Vadula presented the effect of current sensing delay under different operating conditions [1]. Kato proposed a compensation algorithm of the control delay [22], which is operated with single and three phase grid-connected inverter. For voltage source converters, Alberto R C presented a small-signal model, which includes time delays implementation effects [19]. For the purpose of compensating for the delay, Mo modified a PI or PID control algorithm by using the Smith predictor [9]. Based on analyzing the mathematical model of the virtual flux algorithm, Zhang presented a virtual flux observer with negative feedback resonant filter [10]. Cao proposed a control method which is modified predictive current controller based on weighted filter predictor and robust adaptive voltage compensator [2]. Zhang research on the impact of delay and data dropout on stability and performance [29], and presented a power-sharing method for parallel inverter operated via CAN bus communication. Zhao worked on PWM upload delay and zero-order holder delay [7], eliminated the half beat delay of PWM upload and the inner active damping loop delay around resonant frequency by composing PWM real-time upload and first-order high pass filter. For PI controller, Hakan Gündüz analyzed delay stability of microgrid systems [8], then proposed a method that determine stability delay margins in terms of system and controller parameters.

For single-phase LCL-type grid-connected inverters, Zhu worked on the LCL filter [16], focused on the shortcomings of traditional compensation methods for the control delay, proposed a method that based on non-instantaneous loading and pulse-width equivalence. In order to enhance the adaptability of LCL-filtered grid-connected inverters, Li proposed an improved capacitor voltage-feedforward control method with compensating delay [25]. Lyu used the Nyquist diagram to analyze the stability considering the delay effect [27]. Wang analyzed the relationship between delay and stability of grid-connected inverters based on inverter current feedback and grid current feedback [13], and derived the delay range of system stability. Ben Saïd-Romdhane proposed a design method of PI control associated with the capacitor current inner loop active damping [17].

Because of the predictive control is sensitive to delays, based on model predictive control, Mirzaeva proposed method for compensation of delays [6], resulting in improved reference tracking and disturbance rejection, for three-phase inverters, Zhang also proposed a model predictive current control method with delay compensation [3]. Castello used a structure of n cascaded observers to ensure a virtually deadbeat transient response and high stability margins [11]. Due to the high time complexity of finite control set model predictive control(FCSMPC), Chen and Yang both presented a modified FCSMPC method in order to compensate the delay [24, 28].

Based on the analysis of the above references, this paper studies the structure of AC microgrid inverter based on Zigbee wireless communication network, as shown in Fig. 1. Then the control block diagram of the inverter network control system is shown in Fig. 2, where e^-τ_CAs is the control delay and e^-τ_SCs is the network transmission delay. In the existing literature reports, almost all the studies on the control delay or the delay in one sampling period. But in reality, the transmission delay is much larger than this. It is very valuable that investigating the impact of transmission delay in networked control inverters, which can be seen as a major contribution of this research. a compound control method (internal model control and quasi-PR control) of networked control inverter. In this paper, a compound control method (internal model control and quasi-PR control) of networked control inverter is proposed, which can minimize the delay caused by the introduction of the network. In this method, the internal model control is used to minimize the negative effects of the network transmission delay, and the PR control with resonance compensation is used to eliminate the caused by the inverter power circuit. And the design method of parameter in compound controller is presented.

Fig. 1

Structure of AC microgrid inverter based on Zigbee wireless communication network.

Fig. 2

Block diagram of the inverter network control system.

The structure of this paper is as follows. Part 2 introduces the model of the inverter, and theoretically analyzes the mechanism of delay affecting the output performance of the inverter. Part 3 proposes parameter design method for internal model control and PR control. Part 4 provides the simulation results. First, the single inverter with or without delay and operating in proposed compound control method. Second, two parallel inverters simulation comparison between PQ droop control and proposed algorithm. Third, dynamic performance is showed. Part 5 provides the experimental results as the same operating condition with simulation. Part 6 concludes the contribution of this paper.

2 Grid-connected inverters based on networked control system

In order to study the network control system of the microgrid, the microgrid is composed of parallel grid-connected inverter modules, and the information transmission between the inverters is realized by Zigbee wireless communication node.

2.1 System structure

The structure of the grid-connected inverter system is Fig. 3. The rated voltage of the DC side of the system is 400 V, which is obtained by the DC/DC booster circuit. The inverter bridge output is connected to the grid via an inductor L and a grid-connected switch. The inductor is used to filter the high-order harmonic current caused by the switching action, leading to a sine wave with the same frequency as the grid voltage. The system control algorithm is implemented by TI’s floating-point DSP TMS320F28335. The digital soft phase lock is implemented in the DSP to achieve synchronization with the grid frequency and phase. The SPWM logic control signal required for the inverter to operate in parallel is generated. The control of the inverter switch is realized by the isolated driving circuit, so that the inverter can be connected to the grid.

Fig. 3

Model of the three phase inverter.

2.2 Inverter’s model

The three-phase inverter circuit model is shown in Fig. 3.

In the Fig. 3, L_f is the filter inductor, C_f is the filter capacitor, and R_f is ESR. The circuit equation is: ${\begin{matrix} e_{K} + i_{LK} Z_{L} = U_{K} \\ (i_{LK} - i_{gK}) Z_{C} = U_{C} \\ U_{C} + i_{LK} Z_{L} = U_{K} \\ U_{K} = u_{k} + U_{DD} \\ u_{k} = S_{K} \frac{U_{DC}}{2}, (S_{K} = \pm 1) \end{matrix}$ (1)

In the formula, K = a, b, c; e_K is the grid voltage, i_LK is the inductor current of each phase, i_gK is the grid-connected current of each phase, U_C is the capacitor voltage, Z_C, Z_L is the capacitance and inductance impedance. After derivation, the average switching function model can be derived as:

$e_{K} + \frac{Z_{C} Z_{L}}{Z_{C} + 1} i_{gK} = (\frac{U_{DC}}{2} S_{K} + U_{DD}) (1 + \frac{Z_{L}}{Z_{C} + 1})$ (2)

After the Clark transformation, ${\begin{matrix} e_{α} + \frac{Z_{C} Z_{L}}{Z_{C} + 1} i_{gK α} = \frac{U_{DC}}{2} S_{α} (1 + \frac{Z_{L}}{Z_{C} + 1}) \\ e_{β} + \frac{Z_{C} Z_{L}}{Z_{C} + 1} i_{gK β} = \frac{U_{DC}}{2} S_{β} (1 + \frac{Z_{L}}{Z_{C} + 1}) \end{matrix}$ (3)

2.3 Networked control inverters

In the microgrid, a simplified networked control system consisting of a plurality of distributed inverters and controllers is shown in Fig. 2. In the inverter parallel network control system, the controller receives control signals sent by other inverters or remote controllers to realize parallel operation or remote control of the inverter, and the function of the sensor is realized by the sampling circuit of the controller. Concequently, compared with the traditional network control system, only the information transmission delay between the inverters or the delay from the remote controller is considered.

Since the introduction of digital control will bring AD sampling delay, the processor calculates the cycle delay, etc., which is equal to the time difference between the sampling time of the digital-to-analog conversion chip and the loading of the controller output to the pulse width modulation module. The delay is far less than the network induced delay, so it can be neglected. When analyzing the network controlled inverter, only the network-induced delay can be considered, which is equivalent to a pure delay.

The total dead time in a network-controlled inverter system is: $T_{d} = T_{d}^{'} - (T_{on} + T_{off}) + (τ_{CA} + τ_{SC})$ (4)

Where:T_on, T_off is turn-on and turn-off delay of switch, $T_{d}^{'}$ is control dead time, τ_SC is transmission delay, τ_CA is control delay.

Assuming that the inverter carrier ratio is sufficiently high, and there is an equal interval distribution of the error pulses in one switching cycle, the magnitude of the total error pulse amplitude U_eM can be equivalently expressed as $U_{eM} = f_{c} U_{dc} T_{d}$ (5)

The expression fundamental wave of ideal PWM wave u and error wave u_error is

$\begin{matrix} U_{error} = \frac{4 U_{eM}}{π} [sin ω t - \frac{1}{5} sin 5 ω t + \frac{1}{7} sin 7 ω t \dots \dots] \\ = \frac{4 f_{c} U_{dc} T_{d}}{π} [sin ω t + \frac{1}{n} \sum n = 6 k \pm 1 (- 1)^{n} sin n ω t] \end{matrix}$ (6)

It can be obtained that the amplitude U_Mn of the n-th harmonic after passing the filter is

$\begin{matrix} U_{Mn} & = \frac{4 f_{c} U_{dc} T_{d}}{n π} G (ω) \\ = \frac{4 f_{c} U_{dc} T_{d}}{n π} [\frac{1}{LCs (ω)^{2} + rCs (ω) + 1}] \end{matrix}$ (7)

Then $THD = \frac{\sqrt{U_{m 5}^{2} + U_{m 7}^{2} + \dots \dots}}{U_{m 1}}$ (8)

It can be seen from the theoretical derivation that the distortion rate of the inverter output current waveform is directly proportional to the dead time. When other conditions are determined, the transmission delay increases, the dead time increases, and the total harmonic distortion rate of the inverter output current waveform will increase accordingly.

2.4 Control strategy of internal model controller

The composite control system is a control system that combines two or more control systems. The purpose of the composite control is to make the system both stable to the open-loop control system and to the accuracy of the closed-loop control system. Figure 4 is a block diagram of the composite control method proposed in this paper., R(s) and Y(s) are the input and output of the system, G_IMC (s) is internal model controller,G_MRC (s) quasi-PR controller with multiple resonance compensation, the actuator is inverter, τ_SC is Zigbee wireless network transmission delay, e^-τ_CAs is control delay.

Fig. 4

Block diagram of compound control methodology.

In Fig. 5, R(s) and Y(s) are the input and output of the system, N(s) is the system disturbance, G_M (s) is the internal model of the control object, G_F (s) is filter. Available from Fig. 5

Fig. 5

Block diagram of internal model controller.

$\begin{matrix} Y (s) = & \frac{G_{IMC} (s) e^{- τ_{CA} S} G (s)}{1 + G_{IMC} (s) e^{- τ_{CA} s} [G (s) - G_{M} (s)] e^{- τ_{SC} S} G_{F} (s)} R (s) \\ + \frac{1 - G_{IMC} (s) e^{- τ_{CA} s} G_{M} (s) e^{- τ_{SC} s}}{1 + G_{IMC} (s) e^{- τ_{CA} s} [G (s) - G_{M} (s)] e^{- τ_{SC} S} G_{F} (s)} N (s) \end{matrix}$ (10)

Change form

$\frac{Y (s)}{R (s)} = \frac{G_{IMC} (s) e^{- τ_{CA} s} G (s)}{1 + G_{IMC} (s) e^{- τ_{CA} s} [G (s) - G_{M} (s)] e^{- τ_{SC} S} G_{F} (s)}$ (11)

When G (s) = G_M (s), the controlled object completely matches the internal model. $\frac{Y (s)}{R (s)} = G_{IMC} (s) e^{- τ_{CA} s} G (s)$ (12)

As shown in Fig. 6, all delay index terms affecting system stability have been eliminated from the denominator of the closed-loop transfer function, and the delay does not affect the stability of the system.

Fig. 6

Block diagram of Equation 12.

2.5 Control strategy of quasi-PR controller

The proportional resonant controller adds two fixed-frequency closed-loop poles to the axis of the controller transfer function to form a resonance at that frequency, thereby increasing the gain at that frequency point (theoretically, the resonance makes the gain at the design frequency Approaching infinity), achieving the unsynchronized tracking of the sinusoidal command signal at this frequency overcomes the insufficiency of the PI controller to track the sinusoidal signal without static difference. In proportional resonance control, a resonant frequency is also required, from the mathematical essence. The above is consistent, that is, the angular velocity of the synchronous rotation is obtained. The proportional resonance control uses the resonance control equivalent to eliminate the coordinate system transformation process, so that this control method can perform the tracking of the sinusoidal command signal of a specific frequency without difference. $G_{PR} = K_{P} + \frac{K_{R} s}{s^{2} + ω_{0}^{2}}$ (13)

However, in actual system, the ideal PR controller is difficult to implement. At the same time, due to its narrow bandwidth, the system can not achieve no steady-state error tracking when the grid frequency changes. Therefore, this paper uses Quasi-PR to improve the adaptability to the grid frequency offset, and is easy to implement. The transfer function of Quasi-PR is: $G_{QPR} = K_{P} + \frac{2 K_{R} ω_{C} s}{s^{2} + 2 ω_{C} s + ω_{0}^{2}}$ (14)

Where: K_P and K_R are the proportional coefficient and the resonance coefficient, respectively, ω₀ is the resonant frequency, and ω_C is the cutoff frequency.

In order to reduce the harmonic component of the inverter output and achieve the purpose of improving the output waveform, a special harmonic compensator is set in the quasi-proportional resonance controller of the inverter for the low-order odd-numbered harmonics that need to be suppressed to meet the grid connection. Claim. The quasi-proportional resonance controller with harmonic compensator transfer function is: $G_{MRC} = K_{P} + \sum_{n = 1, 3, 5, 7, 9} \frac{2 K_{R} ω_{C} s}{s^{2} + 2 ω_{C} s + {(n ω_{0})}^{2}}$ (15)

The structure of the grid-connected inverter control system is shown in Fig. 7. The MPP reference voltage $U_{dc}^{*}$ can be obtained by the MPPT algorithm, the difference between the measured voltage and the measured voltage is stabilized by the PI controller, and the input current amplitudei_P is obtained. The phase obtained by the phase-locked loop is multiplied to obtain the current reference $i_{a, b, c}^{*}$ , which is obtained by the abc axis to αβ axis transformation. The measured value i_α,β is used as the modulation signal by the Quasi-PR controller in the two-phase stationary coordinate system. After filtering, it can be realized. The grid current has no static tracking.

Fig. 7

Block diagram of control strategy.

3 Controller design

Aiming at the problem of increasing THD output of grid-connected inverter after introducing network control system, this paper presents a design scheme of composite control (internal model control and quasi-proportional resonant controller with harmonic compensator) to suppress the increase of THD.

3.1 Internal model controller

As shown in Fig. 5, First, the internal model of the controlled object is decomposed into two parts: $G_{M} (s) = G_{M 0} (s) G_{M +} (s)$

Where: G_M0 (s) is minimum phase portion, G_M+ (s) is irreversible part, that is all the delays and poles in G_M (s) are located in the right half plane.

According to the H₂ optimal control theory, $G_{IMC} (s) = G_{M 0}^{- 1} (s) = G_{f}^{- 1} (s)$ .

Here, the filter is employ as a second-order low-pass filter. $G_{F} (s) = \frac{ω_{n}^{2}}{s^{2} + 2 ω_{n} s + ω_{n}^{2}}$ (16)

Derived from knowledge of automatic control, let = 0.707, ω_n = 2πf_n, (20f < f_n < 0.5f_S). When the feedback filter and the input filter parameters are the same, it is equivalent to inserting a pre-filter in front of the controller, and the pre-filter can be combined with the feedback filter. At this time, the filter has the function of feedback and input filter.

3.2 Current loop

According to the previous section, the current inner loop control structure of the system can be drawn as shown in Fig. 8.

Fig. 8

Control structure of current loop.

According to the control block diagram, the current loop transfer function is:

$\begin{matrix} {{[i^{*} - i_{gK} e^{- τ}] G_{MRC} K_{PWM} (1 + \frac{Z_{L}}{Z_{C} + 1})} \\ - e_{K}} \frac{Z_{C} + 1}{Z_{C} Z_{L}} = i_{gK} \end{matrix}$ (17)

Since the switching frequency is much higher than the fundamental frequency, the inverter bridge part can be regarded as a proportional link, and the proportional coefficient is K_PWM. If K_PWM = 1, Then the formula 17 can be converted into:

$\begin{matrix} i_{gK} = & i^{*} (s) G_{MRC} (s) \\ \frac{{LC}^{2} s^{2} + C^{2} s + C}{LCS + e^{- τ s} G_{MRC} (s) ({LC}^{2} s^{2} + C^{2} s + C)} \\ - e^{- τ s} \frac{C^{2} s + C}{LCS + e^{- τ s} G_{MRC} (s) ({LC}^{2} s^{2} + C^{2} s + C)} \end{matrix}$ (18)

3.3 Stability analysis of quasi-PR controller

Since the order of the quasi-PR controller system is high, and the system order is further increased after the addition of the resonant controller, the control parameters are too cumbersome. In order to simplify the design, according to the system Bode diagram, the selected parameter range is comprehensively considered, and the stability check is performed in combination with the root trajectory curve and the Bode diagram.

According to Equation 14, the transfer function of the quasi-proportional resonance controller with harmonic compensator contains three variables of K_p, K_r, ω_C. As the basis for parameter adjustment, it is first necessary to understand the influence of each parameter on the system characteristics. Using the control variable method to analyze, control two of the parameters unchanged, analyze the impact of the third parameter change on the system.

Let K_r = 1, ω_C = 5, K_p = 1, 10, 100, the controller Bode diagram is shown in Fig. 9, the blue/green/red line in the figure is K_p = 1, 10, 100 respectively. As can be seen from the figure, with the addition of K_p, the controller increases the gain at and around the resonance frequency, and the gain rate of the resonance frequency point and its vicinity is slower than other frequencies. When K_p increases to a certain extent, the controller reaches saturation and its amplitude-frequency characteristic curve will become a horizontal straight line.

Fig. 9

Bode diagram of K_p = 1, 10, 100.

Let K_P = 1, ω_C = 5, K_r = 1, 10, 100, the controller Bode diagram is shown in Fig. 10, the blue/green/red line in the figure is K_r = 1, 10, 100 respectively. It can be seen from the figure that with the increase of K_r, the controller increases the benefit at the resonance frequency point and the vicinity of the point, and the bandwidth increases, Therefore, the addition of K_r is beneficial to improve the control precision.

Fig. 10

Bode diagram of K_r = 1, 10, 100.

Let K_P = 1, K_r = 1, ω_C = 1, 5, 10 the controller Bode diagram is shown in Fig. 11, the blue/green/red line in the figure is ω_C = 1, 5, 10 respectively. As can be seen from the figure, ω_C not only affects the gain, but also affects the bandwidth. As ω_C increases, both gain and bandwidth increase. But at the resonant frequency point, ω_C does not change the gain. Substituting s = jω into the transfer function, according to the definition of the bandwidth, when $| G (j ω) | = \frac{K_{r}}{\sqrt{2}}$ , the difference between the two frequencies calculated at this time is the bandwidth. Let $| \frac{(ω^{2} - ω_{0}^{2})}{2 ω_{c} ω} | = 1$ , after calculation, the bandwidth of the quasi-resonant controller is: $\frac{ω_{c}}{π}$ , according to the national standard, the allowable fluctuation range of the grid voltage frequency For±0.5 Hz, there is $\frac{ω_{C}}{π} = 1$ Hz, that is ω_C = 3.14 Hz.

Fig. 11

Bode diagram of ω_C = 1, 5, 10.

Summarizing the above analysis, the conclusions about the influence of K_p, K_r, ω_C on the controller are: K_p, K_r affects the resonance gain, and increases K_p, K_r is beneficial to improve the control accuracy, and only K_r is added. Increasing the resonance point benefits, and adding K_p will lift all the benefits; ω_C affects the bandwidth near the resonance point, and the bandwidth of ω_C increases, which makes the system adapt to frequency fluctuations, but the bandwidth should not be too large, so as to avoid nearby frequencies. And ω_C can be calculate according to the allowable fluctuation range of the grid voltage frequency. At the same time, due to the addition of a resonant controller of the corresponding frequency, multiple specific harmonics can be eliminated.

Let K_p = 1, K_r = 1000, ω_C = 3.14, the root locus of the controller is shown in Fig. 12. It can be seen from the figure that all closed-loop poles are located in the left half plane of s, so the system is stable; according to automatic control. The theory requires that the system is fast, and the dominant pole should be far away from the virtual axis. From the figure, the gain is 2.47. To make the system stable and the oscillation is small, the pole is preferably located in the s plane and the negative real axis. Near the ±45° line, so the damping ratio is 0.707. At this time, the stability and rapidity of the system are ideal. From the figure, the gain is 1.43.

Fig. 12

Root locus map of K_p = 1, K_r = 1000, ω_C = 3.14.

4 Simulation

In this paper, a three-phase grid-connected inverter with composite controller is used for simulation comparison. The simulation parameters are shown in Table 1. If not specified the two inverters use the same parameters.

Table 1
Table of simulation parameter

Parameter Value Parameter Value

DC bus voltage U_dc/V 700 Filter inductor L_f/mH 2

AC rated voltage U_N/V 311 Filter capacitor C_f/uF 20

Droop factor m 0.001 Droop factor n 0.002

Switching frequency f_s/kHz 10 Rated angular frequency ω₀/rad/s 314

Scale factor K_P 1.43 Cut-off frequency ω_C/rad/s 3.14

Resonance factor K_r 1430 Cut-off frequency ω_n/rad/s 3000

Parameter	Value	Parameter	Value
DC bus voltage U_dc/V	700	Filter inductor L_f/mH	2
AC rated voltage U_N/V	311	Filter capacitor C_f/uF	20
Droop factor m	0.001	Droop factor n	0.002
Switching frequency f_s/kHz	10	Rated angular frequency ω₀/rad/s	314
Scale factor K_P	1.43	Cut-off frequency ω_C/rad/s	3.14
Resonance factor K_r	1430	Cut-off frequency ω_n/rad/s	3000

4.1 Single inverter with composite controller simulation comparison

Firstly, the composite control is used to simulate the local control and networked control of the single-phase three-phase grid-connected inverter, and then the composite control is simulated, and the output current waveforms under these three operating conditions are One phase is subjected to FFT analysis to compare the harmonic suppression characteristics of the output waveform.

In Fig. 13, figures a, c, and e are current and voltage waveforms of three working conditions, and the grid power factors are all 1. figures b, d, and f are corresponding FFT analysis. It can be seen from the simulation results that the graphs a and b are the output waveform and harmonic analysis of the inverter under the quasi-PR control. The voltage and current waveforms have good sinusoidality and the phase frequency is the same. The voltage amplitude is 311 V and the current amplitude is 20 A., THD is 0.36%; Figures c, d are the output waveform and harmonic analysis of the networked inverter quasi-PR control, the voltage waveform has good sine, the current waveform is worse than the graph a, the phase frequency is the same, the voltage amplitude The value is 311 V, the current amplitude is 20 A, and the THD is 6.81, which is higher than the operation condition of Figure a; Figure e and f are the output waveform and harmonic analysis of the networked inverter under the composite controller, voltage and current respectively. The waveform has a good sine, which is better than the case of Figure c. The phase frequency is the same. The voltage amplitude is 311 V, the current amplitude is 20 A, and the THD is 2.20, which is lower than the case of Figure c. Comparing the simulation results, the following conclusions can be obtained. The output current of the inverter under the quasi-PR control is close to the given current, and the zero steady-state error is basically realized, and the current distortion is small; and the networked inverter under the pseudo-PR control Due to the delay in the control process, although the zero steady-state error is basically realized, the THD has increased from 0.36 to 6.81, which has exceeded the standard that the inverter grid-connected current THD is lower than 5; in order to solve the problem of THD increase, In this paper, the composite control is used to suppress the harmonic distortion of the grid-connected current, and the zero-steady-state error is realized while suppressing the harmonic distortion of the grid-connected current. The output current THD of the networked inverter is from 6.81. It is reduced to 2.20, but because the PADE polynomial method is used to approximate the delay in the control process, the specific harmonics cannot be eliminated perfectly.

Fig. 13

Voltage and current waveforms and harmonic suppression characteristics.

4.2 Parallel inverter simulation comparison

The two inverters controlled by PQ droop and the two networked control inverters are Simulated, and the voltage and current waveforms at the PCC are compared, the output current waveform of each inverter, and the circulating waveforms of the two inverters are compared. Each inverter output waveform FFT analysis.

Figure 14 is a parallel waveform of two inverters controlled by PQ droop, with a droop coefficient m of 0.001 and a droop coefficient n of 0.002. Figure 15 shows the parallel waveforms of two inverters with proposed method, the delay is 20 ms. It can be seen from the figure that the steady-state error, circulation and THD of the networked inverter parallel system are smaller than the PQ droop control.

Fig. 14

Parallel inverters with PQ droop control.

Fig. 15

Parallel inverters with proposed method.

4.3 Dynamic performance simulation

The networked control inverters under proposed method are respectively subjected to off-grid/grid, and the dynamic performance under load/deload conditions is simulated, the delay is 20 ms.

Figure 16 shows the output voltage and current waveforms under four operating conditions with high sinusoidal and low steady-state error. Figure a is the grid-connected waveform. The grid is connected to the grid at 0.3 s. The current waveform starts from the zero crossing point and reaches the steady state in two cycles. Figure b shows the off-grid waveform. The grid starts off-grid at 0.6 s. The current waveform starts from zero crossing. It has a slight impact on the voltage and reaches the steady state in two cycles; Figure c is the reduced carrier shape, the load is reduced from 5 kW to 2.5 kW at 0.4 s, the current waveform changes from the zero crossing point, and the steady state is reached in one cycle. Figure d is the loading waveform. When the load is increased from 5 kW to 10 kW at 0.4 s, the current waveform changes from the zero crossing point and reaches the steady state in one cycle. It is verified that the proposed control algorithm has good dynamic performance.

Fig. 16

Dynamic performance simulation.

5 Experimental

According to the same parameters as the simulation, the three inverters are connected in parallel, and the dead zone of the switch is 1μs. The above conditions are verified by experiments. The electrical and communication connection as shown in Fig. 17, experimental prototype is shown in Fig. 18. The three inverter controllers use TMS320LF2407 and TMS320F28335, the communication platform uses Zigbee wireless communication network, inverters 1 and 2 nodes are directly linked, and the transmission delay is about 9.606 ms; inverters 1 and 3 pass through two Relay node link, its transmission delay is about 17.601 ms.

Fig. 17

Experimental electrical and communication connection diagram.

Fig. 18

Photo of experimental prototype.

Figures 19, 20 correspond to Figs. 14 and 15, respectively. Figure 18 is a parallel waveform of three inverters controlled by PQ droop, with a droop coefficient m of 0.001 and a droop coefficient n of 0.002. Figure 19 shows the parallel waveforms of three inverters controlled by proposed method. The control signals are transmitted through the Zigbee wireless network. It can be seen from the figure that the steady-state error, circulation and THD of the networked inverter parallel system are less than PQ drooping. Control, consistent with the simulation results.

Fig. 19

Parallel inverters with PQ droop control.

Fig. 20

Parallel inverters with proposed method.

Figure 21 is an experimental waveform corresponding to the four operating conditions of Fig. 16. Figure a is the grid-connected waveform. The current waveform starts from the zero-crossing point and reaches the steady state in one cycle. Figure b shows the off-grid waveform. The current waveform returns to zero from the zero-crossing point and reaches the steady state in two cycles. In order to reduce the carrier shape, the current amplitude is reduced from 7.05 A to 3.51 A, the current waveform changes from the zero crossing point, and the steady state is reached in one cycle; the graph d is the loading waveform, the current amplitude is increased from 7.01 A to 14.1 A, and the current waveform starts from the zero crossing point. The change, reaching steady state in one cycle, verifies the effectiveness of the proposed control algorithm.

Fig. 21

Experimental of dynamic performance.

6 Conclusion

This paper has investigated the output characteristics of grid-connected inverter network control system in AC microgrid. The mechanism that the output current THD of the inverter will increasing caused by the network delay is analyzed. A composite control (internal model control and PR control) method for overcoming the increase of THD is proposed, which can overcoming the delay caused by the introduction of the network. And this method improves the accuracy of the output current and can reduce the circumfluence in the wireless parallel system of the inverter. In this method, the internal model control is used to minimize the negative effects of the network delay, and the PR control with resonance compensation is used to eliminate the low-order harmonics brought by the inverter power circuit. The THD and circulation are reduced. Finally, by comparing with the PQ droop control method, the simulation and experimental results are given, and the effectiveness of the proposed control method is demonstrated.

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