BP Neural Network-Based Adaptive Phase-Locked Loop for Impedance Measurement with Dynamic Operating Conditions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper proposes an adaptive phase-locked loop (PLL) design method based on a back-propagation (BP) neural network to address the instability issues in grid-following (GFL) converters during frequency-sweep impedance measurement, which arise from the inability of conventional PLLs to cope with multi-frequency disturbances. The core of the method lies in embedding a neural network into the traditional PI controller to achieve dynamic adaptive adjustment of the PI parameters, thereby enhancing the synchronization performance and stability of the system under complex operating conditions such as dynamic, multi-frequency, and weak-grid scenarios. The effectiveness of the proposed method is validated through simulation and hardware-in-the-loop (HIL) experiments. However, the following questions must be answered:

1. Although Section 4 of the paper presents a stability analysis based on an impedance model, this analysis is conducted using a fixed-parameter linearized model and does not incorporate the dynamic adjustment process of the neural network. It is recommended that the authors supplement the analysis by: 1) approximating the neural network as a dynamic element and analyzing its impact on the system loop gain, phase margin, and gain margin.

2. The use of a three-layer BP neural network for online inference and weight updates inevitably introduces additional computational delay. In control loops such as the PLL, which have extremely high real-time requirements, this computational delay can be equivalent to introducing a detrimental lag into the control loop, thereby affecting stability, especially in high-frequency bands. While the paper mentions setting a threshold to reduce computational burden, it does not quantitatively analyze the worst-case execution time (WCET) of the neural network or its specific impact on the system stability margin. It is recommended that the authors measure or estimate the actual execution time of the neural network module in HIL experiments.

Author Response

1) Although Section 4 of the paper presents a stability analysis based on an impedance model, this analysis is conducted using a fixed-parameter linearized model and does not incorporate the dynamic adjustment process of the neural network. It is recommended that the authors supplement the analysis by: 1) approximating the neural network as a dynamic element and analyzing its impact on the system loop gain, phase margin, and gain margin.

Author response: Thank you for your valuable suggestion. In response to the reviewers' comments, a more detailed analysis has been conducted. The approximate computational process of the online BP neural network is supplemented in Section 3.3. In Section 4.2, the parameter adjustment trend of the online BP neural network is added, and the neural network is further approximated as a time-delay element to analyze and compare the stability margin of the system with BP dynamics considered.

 

2) The use of a three-layer BP neural network for online inference and weight updates inevitably introduces additional computational delay. In control loops such as the PLL, which have extremely high real-time requirements, this computational delay can be equivalent to introducing a detrimental lag into the control loop, thereby affecting stability, especially in high-frequency bands. While the paper mentions setting a threshold to reduce computational burden, it does not quantitatively analyze the worst-case execution time (WCET) of the neural network or its specific impact on the system stability margin. It is recommended that the authors measure or estimate the actual execution time of the neural network module in HIL experiments.

Author response: Thank you for your valuable suggestion. In response to the reviewers' comments, a more detailed analysis has been conducted. A more comprehensive optimization architecture of the BP neural network is supplemented in Section 3.1, where the offline part pre-fits the approximate parameters. The main computation load of the processor stems from the online part. In Section 3.3, the engineering-oriented optimization methods for the online BP computation are added, and the computational complexity is estimated. Additionally, the Hardware-in-the-Loop (HIL) test results based on Rt-box are supplemented in Section 5.3, with the execution time quantified. These results verify that the online computation of the BP neural network does not introduce a time delay that impairs the system operation.

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper, a BP neural network–based adaptive phase-locked loop for impedance measurement under dynamic operating conditions is presented.

The topic has been widely investigated in the literature. However, the novelty of the proposed approach is not clearly stated in the introduction. The following comments are provided:

1. More detailed information on the neural network structure, training procedure, and accuracy should be included. How was the dataset created?

2. The voltages shown in Fig. 21 appear to be affected by distortion. Please evaluate this aspect and verify whether the distortion is acceptable according to relevant standards.

3. Fig. 5 is difficult to read; please increase its size. In addition, each Bode plot should be clearly described in the text.

4. How were the values reported in Table 1 selected? Please provide a justification.

Author Response

1) More detailed information on the neural network structure, training procedure, and accuracy should be included. How was the dataset created?

Author response: Thank you for your valuable suggestion. In response to the reviewers' comments, a more detailed analysis has been conducted. A more comprehensive optimization architecture for the neural network control is supplemented in Section 3.1 of this paper, which is divided into an offline part and an online part with a three-layer structure for both. The dataset for the offline part is obtained from a large number of preliminary experiments, and the samples are expanded via transfer learning. Different from the conventional BP neural network, the online part performs real-time computation and fine-tuning based on the gradient descent principle without relying on any dataset. The structure of the BP neural network in the simulations and experiments is also further supplemented in Section 5.

 

2) The voltages shown in Fig. 21 appear to be affected by distortion. Please evaluate this aspect and verify whether the distortion is acceptable according to relevant standards.

Author response: Thank you for your valuable suggestion. Fig. 21 depicts the current waveform of the harmonic injected for impedance measurement by the reconfigurable converter, which contains both the power-frequency current and the harmonic current. In the analysis of control stability optimization, this test has covered the stability scenarios of impedance measurement with the injected harmonic amplitude not exceeding the tested value. In practical applications, the required injection amplitude can be refined in accordance with the grid harmonic injection specifications.

 

3) Fig. 5 is difficult to read; please increase its size. In addition, each Bode plot should be clearly described in the text.

Author response: Thank you for your valuable suggestion. In response to the reviewers' comments, we have made detailed revisions. Specifically, the negative impedance frequency band has been added to Fig. 5, and a more detailed description of this figure has been supplemented in the text.

 

4) How were the values reported in Table 1 selected? Please provide a justification.

Author response: Thank you for your valuable suggestion. In response to the reviewers' comments, we have provided a detailed explanation of the selection and design specifications for the parameters in Table 1 in Section 2.1. 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed all reviewer comments, corrected the identified errors, and incorporated the relevant additional content. The revised manuscript is now ready for publication.

Reviewer 2 Report

Comments and Suggestions for Authors

The concerns have been addressed.