Embedding OFDM-Based Carrier Communication Into Power Control Loop of Converter in DC Microgrids

In direct current (dc) microgrids, communication between converters is necessary for better power distribution and finer energy scheduling. This article proposes an orthogonal frequency division multiplexing (OFDM) based carrier communication method for dc microgrid applications. The method integrates the communication function in the process of power conversion by modulating data into power control loop. To maximize the communication rate in a narrow band limited by pulsewidth modulation control, OFDM technology is applied in the data modulation process. The data is modulated to multiple low-frequency signal carriers, then the modulated wave is added to the output of the power control loop. Since no additional component is needed for sending data, this method has the advantages of low cost and simple implementation. In order to provide theoretical guidance for system design, the dc microgrid applying the proposed method is modeled. Furthermore, important issues of the communication system are discussed, including data frame format and intersymbol interference problem. At last, a 2 kW dc microgrid experimental platform is established and 9.6 kbps communication rate with a transmission distance of 200 m is achieved, which verifies the feasibility of the proposed method.

proposed. In Section III, the model of the dc microgrid employing the proposed method is set up and the signal transmission gain is analyzed in detail. Furthermore, guidance for power system design is provided. In Section IV, important issues of the communication system are discussed. In Section V, the experiments based on a dc microgrid platform are carried out to verify the correctness of the theory and the feasibility of the proposed method. Finally, conclusions and prospects are given in Section VII.
The main contributions of the article are as follows. 1) For the first time, the OFDM technology is implemented in the PSDM-CL method. A 9.6 kbps communication link is achieved in a 2 kW dc microgrid system with 10 kHz narrow bandwidth, which is significantly faster than the previous PSDM-CL methods in [20]- [22]. 2) A new model of dc microgrid employing the proposed OFDM-based PSDM-CL method is established. The signal transmission gain is analyzed in detail, which offers theoretical guidance for system design. 3) To deal with different and complex communication channel characteristics in the power electronics systems embedding the proposed method, a practical intersymbol interference (ISI) evaluation approach by numerical computation is designed in this article.

A. Principle of PSDM-CL Method
In the proposed PSDM-CL system, the power converter sending out data symbols is named as data-sending converter (DSC), while the power converter receiving data is named as data-receiving converter (DRC). The data modulation process in a DSC is shown in Fig. 1. First, the baseband data is modulated as a perturbance signal s(t). In this procedure, conventional modulation methods, such as FSK, amplitude shift keying, phase shift keying (PSK), and methods of multicarrier modulation, can be employed. Then, s(t) is added to the output of power control loop v p (t) as a PSDM-CL signal v ps (t). Finally, v ps (t) is compared with the triangular carrier v tri (t) to generate a gate drive signal g(t) for the DSC. After these, the data is modulated and merged into g(t).
In a dc microgrid system, PSDM-CL technique can be adopted by the converters for communication. A simplified structure of DC microgrid is shown in Fig. 2. In the system, any converters, including distributed generators (DGs) and power loads (PLs), can operate as a DSC or a DRC.
Generally, a dc-dc converter can be divided into three parts: input low pass filter (LPF), switching network and output LPF. In a DSC, the gate drive signal g(t), which contains data information, is amplified by the switching network as the power pulse A o (t), which is then filtered by the output LPF. Accompanied with electric power, the data symbol is injected into the dc bus. In a DRC, the dc-bus voltage is sampled, and the data can be demodulated.
In PSDM-CL scheme, it is preferable to decouple the control of power transfer and data communication. Thus, in order to suppress the influence of power control on the data symbol, the data carrier frequency f c should be selected above the power control loop cut-off frequency f p . On the other side, mixed in the output power pulse A o (t), the data symbol is attenuated by the output LPF, so f c should be chosen as low as possible for higher transmission gain. Considering the aforementioned factors, the data carrier frequency f c is selected as 1/50-1/5 of the converter's switching frequency f s .
According to above analysis, it can be concluded that the data bandwidth in PSDM-CL scheme is limited in a narrow band. In order to promote the bandwidth efficiency of the communication system, OFDM technique with multiple subcarriers is employed in this article. For each subcarrier, quadrature differential PSK (QDPSK) is selected as the band modulation method. The principles of data modulation and demodulation are discussed as follows.

B. Data Modulation and Demodulation Principle of PSDM-CL Method Based on QDPSK-OFDM
For an OFDM system with N subcarriers x k (t), the modulated signal s(t) of the system can be expressed as x k (t) = d k cos(2πf ck t + ϕ k ), k = 1, 2, . . . , N where x k (t) is the kth subcarrier, and d k , f ck , ϕ k are the amplitude, frequency, and phase of the kth subcarrier, respectively. According to the basis of OFDM, x k (t) should be orthogonal with each other in a single symbol period T b , which is where i, j = 1, 2, …, N, and iࣔj. It can be deduced from (3) that where M k are positive integers. The process of QDPSK-OFDM includes two steps, as shown in Fig. 3. The first step is the serial-to-parallel conversion. The baseband data stream in series is redistributed to N OFDM subcarriers. The second step is the QDPSK modulation. For each subcarrier x k (t), a quadrature bit is converted into M k continuous sinusoidal waves in one symbol period. As the data information of the kth subcarrier in the nth symbol period, dat k [n] determines the phase difference Δϕ k (n) of x k (t) between the nth and (n−1)th symbol period, which is The perturbance signal s(t) is the summation result of all x k (t), which is then added to the power control loop for transmission. Suppose a 16 Quaternary code "0312 1302 3120 1213" is being transmitted in an OFDM system with four subcarriers. The waveform of x k (t) is illustrated in Fig. 4(a). Take the fourth subcarrier x 4 (t) as an example, the transmitted data is "1213," a quadrature bit is converted into four continuous sinusoidal waves in one symbol period. The relationship among ϕ 4 (n), Δϕ 4 (n) and dat 4 [n] are as shown in Fig. 4(b).
Applying the OFDM-based PSDM-CL method in the dc microgrid and ignoring the sidebands, the spectrum of dc-bus voltage v PCC is shown in Fig. 5, where f g is the grid frequency. The frequencies of the subcarriers are orthogonal to one another. They are all far apart from the power transmission band, the grid frequency f g and the switching frequency f s , which alleviates the interference from power harmonics.
The data demodulation process of the PSDM-CL method includes two steps, as shown in Fig. 3. The first step is the discrete Fourier transform (DFT). In the DRC, the dc-bus signal v PCC is sent through a band pass filter (BPF) to eliminate interference. For the kth subcarrier, by performing DFT at f ck on the filtered  signal v fil , the phase in the (n − 1)th and nth symbol period are calculated as θ k (n − 1) and θ k (n) respectively, so the phase difference of the two symbols is Based on QDPSK principle, dat k [n] is got according to Δθ k (n). Finally, parallel-to-serial conversion is performed on all the received data of subcarriers, and the data can be decoded by the DRC.

III. MODELING OF DC MICROGRID APPLYING THE PROPOSED METHOD
In general, the characteristics of the communication channel would affect the performances of communication system. In the dc microgrid system, the impedance of the power electronic converter is the key determinant for the channel characteristics. Thus, it is necessary to model the dc microgrid system and analyze the impedance of the communication channel.
Considering the cable impedance, the equivalent model of a typical dc microgrid system is shown in Fig. 6. The system consists of n 1 DGs and n 2 PLs, and PCC is the point of common coupling in the system. Z l_DGi and Z l_Lj are the equivalent cable impedance from DG #i and PL #j to PCC respectively. The DGs can be simplified by using Thevenin's equivalent theorem, as shown in Fig. 6, where v o_DGi and Z oc_DGi are the voltage source and output impedance of DG #i in Thevenin equivalent model, respectively. For PL #j, the closed-loop input impedance is denoted as Z ic_Lj . Since the distributed cable capacitance is small, it is merged to the input and output impedance of DGs and PLs.
For convenience, assume that the dc microgrid operates in island mode without grid-connected inverters. Suppose DG #1, which is a droop-controlled boost converter, performs as the DSC, and PL #1, which is a buck converter, performs as the DRC. Compared with the power modulation signal, the communication carrier is a small perturbation. Since f c is less than f s /5, the traditional small signal analysis is applicable.
In the proposed method, the duty perturbation at f c in power control loop corresponds to the amplitude of OFDM subcarriers with the same frequency. The signal transmission gain from DSC to DRC, is defined as G sig in (7), whered is the perturbation signal added to the control loop in DSC, andv sig is the signal received by DRC. G sig is the most important parameter for the PSDM-CL system and will be analyzed in detail The detailed control block diagram of DG #1 is illustrated in Fig. 7(a), whereV o1 is the reference voltage without load, and r d is the droop coefficient. The control scheme consists of three loops, the drooped-control outer loop, the voltage loop and the inductor current inner loop. The related transfer functions (TFs) are listed as follows.
G v : Compensation TF of voltage loop. G i : Compensation TF of inductor current loop. G delay : TF of the digital control delay link. G id : TF from the duty cycle to inductor currentî L .
Referring to [24], the expressions of G id , G iio , G vio , and G vi are calculated as in (8), where D p is the duty cycle of S 2 in steady state, I o1 and V o1 are the dc output current and voltage The output impedance of DG #1 can be expressed as (9), where T v and T i are the open-loop gain of the voltage and current control loop, respectively, For DG #i and PL #j, the equivalent impedance Z DGi and Z Lj seen from PCC are Therefore, the equivalent input impedance of the rest converters seen from PCC is So, the load impedance of DG #1 can be written as Since the frequency of data carrier f c is beyond the cut-off frequency of power control loop f p , the branches of the feedback, including droop-control loop, voltage loop and current loop, can be ignored at f c . Thus, the control diagram can be simplified as Fig. 7(b), and the TF betweend andv o1 can be derived aŝ By combining (16) and (17), the signal transmission gain is Ignoring the line impedance, (18) can be simplified as It can be deduced from (19) that |G sig | is determined by the inductance L and capacitance C o of DG #1 at a fixed output power. In the proposed system, capacitor C o should be designed to fit for the required signal strength. The relationship among |G sig |, capacitance C o and carrier frequency f c are shown in Fig. 8. It can be observed that |G sig | decreases as f c increases, which corresponds with the characteristics of output LPF. Also, at a given f c , |G sig | is negatively correlated with C o , which indicates that reducing the capacitance of the converter at the bus port could improve the signal transmission gain.
However, in most applications of dc microgrids, the line impedance cannot be ignored. In this article, the impedance of the power line is assumed to be where l PL1 is the length of the power line in meters, the gainfrequency characteristics of G sig with different l PL1 is plotted in Fig. 9. It can be observed that the communication signal is reduced with the increasing of l PL1 . In addition, the decay rate of |G sig | is about 60 dB/10 dec in frequency domain. Thus, the higher-frequency subcarriers would be attenuated more seriously in the communication channel.
In order to increase the signal transmission gain of highfrequency subcarriers in long-distance applications, an inductor L M can be added at the bus port of the converter, as suggested in Fig. 6. The existence of L M increases Z ic_L1 and thereby increasing |G sig | according to (18). Fig. 10 shows the gainfrequency characteristics with added L M . It can be observed that L M promotes the signal transmission gain at high frequencies.
However, an additional zero at f r is introduced by the resonance of L M and the input capacitor C bus_PL1 of DRC. To reduce the impact on the communication, f r should be assigned to a frequency lower than the OFDM spectrum. Besides, the power transmission band is typically from dc to several hundred hertz. In order to reduce the impact on power control, it is preferable to set f r higher than the power transmission band. The detailed method is out of the scope of this article, and will not be discussed.

A. Frame Format Design
According to the above analysis, the transmission gain and delays of subcarriers in the channel are different, which causes ISI and intercarrier interference (ICI). In OFDM technology, a cyclic prefix (CP) is usually added to eliminate ICI, reduce ISI and improve the signal-to-noise ratio (SNR). This method is adopted by this article, and the communication frame format is shown in Fig. 11. For simplicity, only one subcarrier is plotted. Each frame format consists of one synchronization symbol and N data data symbols. The synchronization symbol and the data symbol (including CP) have the same duration, which is T b . The synchronization symbol performs as the frame header, marking the beginning of a frame. The data is firstly distributed to N subcarriers, and then modulated into the periods of data symbols according to QDPSK principle, as discussed in Section II. The detailed communication process is illustrated as follows.
First, the synchronization symbol is sent from the transmitter to the receiver. The carrier frequency used by the synchronization bit is generally selected among OFDM subcarrier frequencies f c1 ∼f cN . The receiver detects the amplitude of the synchronization signal through a sliding window DFT algorithm to achieve frame synchronization.
Then, N data data symbols are transmitted in sequence. Each data symbol is composed of a CP and a DFT period, denoted as T CP and T DFT respectively. The lengths of CP and DFT period should satisfy The phase of each subcarrier is continuous during T CP and T DFT , which ensures the correctness of demodulation results even if the DFT window at the receiver is not completely aligned with T DFT .
The performance of OFDM communication is greatly affected by system parameters, including subcarrier frequency spacing Δf c and CP length T CP .
In general, the subcarrier spacing Δf c is set with respect to T DFT , which is where M s is a positive integer. In order to achieve maximum band utilization in a narrow band, M s is set to 1 in the proposed method, thus Δf c is 1/T DFT . In order to eliminate ICI caused by the multipath delay of subcarriers in the communication channel, T CP must be greater than the maximum multipath delay, which is

B. ISI Evaluation
Conventionally, ISI for a communication system is analyzed and evaluated in time domain, which is rather complicated. In order to deal with different and complex communication channel characteristics in the power electronics systems with the proposed OFDM-based PSDM-CL technique, a practical ISI evaluation method is designed as following.
In an OFDM system, the subcarrier x k in the nth symbol period suffers interference from previous symbols due to the nonideal characteristic of the communication channel, which is defined as ISI. For subcarrier x k , ISI originates from two parts, which are interference from itself and from other subcarriers. The latter can be easily eliminated by adding a CP, and this article will focus on evaluating ISI from itself.
In general, the ISI is mainly from adjacent symbol. In the nth symbol period, the kth subcarrier signal x k (t) to be transmitted is the result of multiplying the ideal sine wave w k (t) and the rectangular window r 1 (t) in time domain, as shown in Fig. 12 x The expression of r 1 (t) is The TF of the channel is composed of signal transmission gain G sig (ω) and the signal filter G fil (ω) at the receiver. Passing through the channel, the received signal y k (t) is (26) By performing DFT algorithm on y k (t), the demodulated results at f ck in the nth symbol period can be calculated as The nth symbol will interfere the demodulation of the (n+1)th symbol. By adding a delayed rectangular window r 2 (t) to y k (t) and performing DFT, the received signal can be calculated as The relationship between r 2 (t) and r 1 (t) is The analytical expressions of (27) and (28) are often complex or even unsolvable. Therefore, in practical, numerical calculation tools such as MATLAB can be used to calculate Y R1 (ω) and Y R2 (ω). Define α as Obviously α represents the severity of ISI. The higher the value of α, the more serious the ISI problem will be. The ISI of the proposed system will be evaluated in Section V-A by calculating α and the maximum angle error θ e .

A. Experimental Setup
The feasibility of the PSDM-CL method and the correctness of the theoretical analysis have been experimentally verified on a 2 kW dc microgrid experimental platform. The platform structure and photo are shown in Figs. 13 and 14, respectively. The dc microgrid includes two DGs with boost topology and two PLs with buck topology. DG #1 performs as DSC and PL #1 performs as DRC. TMS320F28377 from Texas Instruments is used for each power converter to implement the control algorithm and the proposed OFDM-based PSDM-CL method. 200-meters cables are used to connect PCC and PL #1 to test the communication performance with long cables.  The experimental parameters of the dc microgrid and the communication system are given in Tables I and II, respectively. It should be noted that L M is only for the experiment in Section V-D. In this platform, the converter's power control loop cut-off frequency is set to 2 kHz, while the communication carrier frequencies are selected above 3 kHz to decouple power conversion and data communication.
In order to meet the communication rate requirement of secondary control in dc microgrid, the DFT period is set to 1 ms. Besides, the frame duration is 12 ms, which is much less than 100 ms, i.e., the real-time transmission requirement of secondary control. According to (23), the maximum multipath delay is 0.089 ms. Thus, a CP T CP is set to 0.2 ms to eliminate ICI. Six subcarriers x 1 ∼x 6 are used for OFDM modulation on DG #1 and each subcarrier is modulated by QDPSK. Thus, each subcarrier in one frame contains 16-bits data information according to QDPSK principle. The communication baud rate of the experimental platform is Before the experimental study, a MATLAB/Simulink model of the communication system is built to evaluate ISI based on Section IV-C. Based on the simulation results, the relationship among α, θ e and f ck is plotted in Fig. 15(a). It can be observed that the severity of ISI decreases as f c increases. The maximum angle error caused by ISI is 7.56°, which is much smaller than 45°. Hence, the SNR can be guaranteed when QDPSK is applied in the experiment.

B. System Modeling Experimental Verification
This experiment aims to check the correctness of system modeling in Section III. In this test, the length of the cable l PL1 is 1 meter. The peak value ofv sig is measured at PL #1 when perturbationd is added to the control loop in DG #1. The theoretical and experimental results of |G sig | are calculated and plotted, as shown in Fig. 15(b). It can be observed that the experimental result is almost in line with the theoretical one, which verifies the correctness of the system modeling. It is also clear that |G sig | gradually decreases as the frequency increases. In order to compensate for the attenuation of higher-frequency subcarriers, a viable option is to increase the perturbation amplitudes of higher-frequency subcarriers.

C. System Performance Test With Short Cable
In this experiment, the power transfer and communication functions of the dc microgrid system are tested. The length of the cable l PL1 = 1 m. The dc microgrid is operated in steady state. DG #1 and DG #2 are transferring a total power of 2 kW to the PLs, and each PL consumes a fixed power of 1 kW.
In this case, DG #1 sends a set of test data dat k [8] 1 repeatedly to other power converters via the dc bus. The subcarrier frequency f ck , perturbance amplitude d k and quaternary data sent by each subcarrier are given in Table III. According to (16), the maximum perturbation of v PCC introduced by the communication is 489 mV. This value meets the power quality requirements of the dc microgrid. Fig. 16 depicts the modulation waveforms of DG #1 when it is sending dat k [8] 1 . x 1 (t) and x 4 (t), which are the first and fourth subcarrier modulation waveforms, respectively, are expressed by the outputs of digital-to-analog conversion (DAC) module. v ps (t) is the DAC output of s(t), which has been explained in Section II. v PCC_DG1 is the ac component of v PCC_DG1 . It can be observed that the carrier frequency used by the synchronization symbol is 3kHz, and the waveforms of x 1 (t), x 4 (t), and v ps (t) are matched with the theory in Section II. Fig. 17 demonstrates the operation states of the dc microgrid. It can be observed that V PCC_DG1 is around 370 V. The ac componentṽ PCC_DG1 has a peak-to-peak amplitude of around 1.2 V. The load current of PL #1 I o_PL1 is about 5A, which corresponds to 1 kW load. The fluctuation of v PCC_DG1 introduced by communication does not exceed 1V. The filtered signal v fil is obtained by passing through a BPF from v PCC_PL1 , and it is ready for demodulation.
At PL #1, demodulation algorithm is performed by the microcontroller, and the results of the subcarrier data are expressed by the outputs of DAC module, as shown in Fig. 18. The results are consistent with Table III, which proves the effectiveness of the proposed communication method. The signals of CH2-CH7 lag about T DFT behind the signal of CH1, which is because the controller needs to perform DFT within a complete T DFT .  Besides, the frequency spectrum of v fil is shown in Fig. 19. The frequency band of the fast Fourier transform results is distributed between 2.5 and 8.5 kHz. The frequency band is relatively flat, which verifies the relevant analysis in Section III.

D. System Performance Test With Long Cable
This experiment aims to test the communication function under the circumstances of long transmission distance. In this case, l PL1 is set to 200 m. In order to increase the input impedance of converters, L M is added at the bus port of every converter.
As an example, a simple communication protocol is designed. In the protocol, subcarrier x 1 and x 2 are arranged to represent the command type and value respectively, while subcarrier x 3 is reserved for the summation check results of x 1 and x 2 . Subcarrier x 4 , x 5 and x 6 are not used in the simple protocol. They can be used in more complicated protocols for advanced dc microgrid secondary control.
In this experiment, DG #1 performs as the master and sends a command frame to change the output power of PL #1 by the proposed OFDM-based PSDM-CL method. The detailed parameters of the command frame are illustrated in Table IV. In order to promote the signal strength at DRC, d k is set larger than that in the experiment of Section V-C. The command type 0x03 in the subcarrier x 1 represents that DG #1 orders PL #1 to regulate its output power to the given value. The given value is 600 W, which is expressed by the subcarrier x 2 . As the slave, PL #1 samples the bus voltage, demodulates the data frame and regulates its output power according to the command. Fig. 20 depicts the waveforms of the above process. v fil is the filtered signal obtained by passing through a BPF from v PCC_PL1 . The initial operation state of dc microgrid is the same as that in Section V-C. The output power of PL #1 is 1 kW. At t 0 , a command frame is sent by DG #1. Starting from t 1 , PL #1 successfully receives the command frame and regulates its output power to 600 W according to the data information.
In order to clarify the details of the communication process, the command frame in Fig. 20 is zoomed in, along with its   demodulation results, as shown in Fig. 21. The demodulation results are the same with dat k [8] 2 in Table IV, which proves the feasibility of the proposed method under the circumstances of long transmission distance.
Furtherly, the enlarged waveforms ofṽ PCC_DG1 and v PCC_PL1 during the communication process are illustrated in Fig. 22. The ac amplitude of v PCC_PL1 is about 2/5 that of v PCC_DG1 , which is consistent with the analysis in Section III. Whereas, due to the existence of L M , the signal is still large enough to be correctly demodulated by the DRC.

VI. CONCLUSION
This article analyzes the principles and implementations of OFDM-based PSDM-CL method and validates its feasibility in the dc microgrid. A practical evaluation method for ISI was designed, which can be promoted to all power electrical systems applying the OFDM-based PSDM-CL method. A communication rate of 9.6 kbps was achieved in a 2 kW dc microgrid, which meets the requirements of microgrid applications. Since no additional communication controllers and less communication components were required by the proposed method, it has the advantages of low costs and simple implementation, and therefore has broad application prospects.
Nevertheless, the proposed method introduced in this article was improved in many aspects. First, advanced techniques used in conventional OFDM, such as equalization and peakto-average-power-ratio suppression techniques, was adopted to deal with complicated operating conditions. Second, in practical, communication failure might occur due to complex power transfer situations. In this case, automatic repeat request mechanism was employed to deal with the communication failure. Third, in long-distance communication applications, additional impedance-match components were required to promote the signal transmission gain of high-frequency subcarriers, which is worth further research.