5.1. Delineation Results
The IEEE-33 bus system distribution network system is used for example analysis. The harmonic current injection of Scenario 1 and Scenario 2 is shown in
Figure A1 and
Figure A2 in the
Appendix A, respectively.
Taking Scenario 1 as an example, the harmonic current data corresponding to each harmonic in Scenario 1 is input into the SPSSAU system, and the optimal sequence diagram method is used to analyze the weight data. The system calculates the average value of each harmonic and uses the average value to construct the matrix. After data processing, the importance of each harmonic in the corresponding scenario is obtained.
In
Table 2, the number 0 is relatively unimportant, the number 1 is relatively more important, and the number 0.5 is equally essential. Compared with the data in the table, the importance of the fifth harmonic in the mitigation system is the highest.
Dex score TTL is obtained by adding the weight value of each harmonic in each row relative to a particular harmonic in
Table 2. For example, the index score TTL5 of the fifth harmonic is 0.5 + 1 + 1 + 1 = 3.5. The TTL of each harmonic is calculated and normalized, and then the specific weight values of the 5th, 7th, 11th, and 13th harmonics in the system are obtained. The calculation results are shown in
Table 3.
Figure 8 shows the specific value of each harmonic weight. Combining the obtained harmonic sensitivity weight with the partition method of the comprehensive sensitivity analysis in
Section 3, the partition results based on comprehensive sensitivity partition can be obtained and finally divided into five regions Region I–Region V. The partition results are shown in
Figure 9.
5.3. Example Solution
This paper assumes that all five mitigation devices are involved in partition adjustment and regional mutual assistance. Taking the sizeable harmonic pollution in Region III as an example, the mitigation device = 1 in Regions I and II is set. It can be seen from Formula (18) that if takes 1, the mitigation device 1 and the mitigation device 2 do not participate in the auxiliary mitigation process of Region III. Only the VDAPF of Region IV and Region V provide compensation capacity for Region III with edge nodes through direct assistance.
Taking the maximum number of devices participating in assisted mitigation as an example, five mitigation devices are set to participate in 200 self-learning processes. The disturbance of the harmonic mitigation system refers to the harmonic current injection of Scenario 2, and the weight coefficient of the system is 0.5. In the absence of early warning, the time interval of each round of assisted adjustment is one minute. The system will be adjusted in real time when the early warning is received.
During the training process, each mitigation device
increases by 0.002 s each time. The growth rate of compensation in the training process is different because of the different enthusiasm of each mitigation device. For example, the
of mitigation device 4 is the smallest, so
is the largest, which is intuitively reflected in the largest growth slope, as shown in
Figure 10. At the same time, if a mitigation device reaches the upper limit of the available compensation capacity during the comigration process, it is compensated according to the maximum compensation capacity, and the compensation capacity of the subsequent training process will not increase again.
Table 5 shows the specific values of the residual capacity and the coefficient corresponding to each mitigation device.
As shown in
Figure 11, when the compensation capacity of the mitigation device is adjusted to the capacity required by the adjacent area, the integral increases. During the 70th training session, the points for all mitigation devices peaked. Because the increase in points is a comprehensive consideration of the two factors of the output of the mitigation device and the mitigation effect, when the compensation capacity of the adjacent area continues to increase, it may lead to an insufficient mitigation capacity of the original mitigation area and affect the mitigation effect of the whole area. At this time, the points of all the mitigation devices gradually decline. In the 170th training session, the No.1 mitigation device with the most sufficient remaining mitigation capacity reaches the upper limit. In summary, the mitigation system takes the best training effect at the 70th training session. At this time, the optimal changes in the conductance of the actual mitigation device are 0.36, 0.28, 0.85, 0.59, and 0.63 S, respectively.
5.4. Comparative Analysis
Relying only on the traditional partitioning method, each VDAPF only governs the harmonic voltage at the mitigation point in the area, and some observation nodes still have a voltage distortion rate exceeding the limit after the partition mitigation under Scenario 2. As shown in
Figure 12, when the partition adjustment is carried out according to the best training effect, the harmonic distortion rates of the observation nodes in Scenario 1 and Scenario 2 align with the mitigation standards after the adjacent mitigation device assists in the mitigation. The harmonic distortion rates of some observation nodes in Scenario 2 that are not qualified by the initial partition mitigation are optimized to be below 4%. This proves the rationality of the above partition adjustment results, and the distributed mitigation system can achieve the ideal mitigation effect through the regional mutual assistance model.
Compared with decentralized mitigation, as shown in
Figure 13, whether it is a slight disturbance or harmonic pollution, the harmonic voltage distortion rate of the observation node after partition adjustment is below 4%, which meets the harmonic voltage mitigation standard. However, there is a situation where the harmonic voltage distortion rate is greater than 4% in decentralized mitigation, which does not meet the standard. To ensure that the voltage distortion rate meets the required standards, augmenting the quantity of mitigation devices is necessary. This approach enhances the mitigation efficacy while concurrently reducing economic costs. It can be seen that reasonable distributed mitigation is superior to decentralized mitigation regarding economy and the mitigation effect.
Based on the harmonic voltage distortion of the node, the harmonic distortion rate of the mitigation node meets the requirements. For several nodes (nodes 6, 25, and 12) with harmonic distortion rates greater than 7% before mitigation, under the incentive model of this section, the VDAPF obtains integral active mitigation, avoiding the waste of resources and maximizing the value of its residual compensation capacity. After the initial partition mitigation, the harmonic voltage distortion rate of node 25 still decreased from 4.5% to 3.5% after collaborative mitigation, and the mitigation effect improved significantly.
In order to further verify the rationality of the collaborative mitigation scheme, the total harmonic voltage distortion rate of each node in the whole network is used as the evaluation standard of the mitigation effect. The simulation is analyzed and verified in the cases of less harmonic pollution in Scenario 1 and heavier harmonic pollution in Scenario 2. Two different harmonic mitigation methods are compared as follows: method 1, harmonic mitigation by comprehensive sensitivity partition, and method 2, VDAPF active output to assist harmonic co-mitigation in adjacent areas.
Comparing the harmonic mitigation effects of the two methods in two scenarios, the mitigation effect of method 2 is better than that of method 1. As shown in
Figure 14, after optimizing the partition mitigation, the
of the edge nodes in Scenario 2 is governed below 4%, which meets the mitigation requirements.
The mitigation effects of the two scenarios are analyzed. Firstly, in Scenario 1, the results of the two mitigation methods are compared, as shown in
Figure 15.
Each node’s total harmonic voltage distortion rate is concentrated at about 7% before mitigation. After mitigation by the two methods, most nodes’ total harmonic voltage distortion rates are kept below 3% for even more than half of the nodes. The total harmonic voltage distortion is at a low level of about 2%, and the curve trend of method 1 and method 2 in
Figure 15 has a high similarity. This shows that the two methods are applicable in the case of light harmonic pollution, and the distributed mitigation system will not issue an early warning request for regional assistance. It is only necessary to adjust each VDAPF output point by periodic optimization. In Scenario 1, the mitigation nodes in each region can mitigate the harmonic voltage of each node by relying on the VDAPF in the region.
The harmonic voltage distortion rate at nodes 3, 6, 13, and 32 is significantly lower than that before mitigation and lower than the voltage distortion of the other nodes because these nodes are more sensitive to harmonic distortion and have higher requirements for voltage distortion than the other nodes. Therefore, in calculating the global effect factor, the sensitivity factor of the above nodes is given an immense value. Finally, the voltage distortion is globally up to standard, and the harmonic voltage distortion rate required by the sensitive nodes is targeted.
The effect of the two mitigation methods under the harmonic current injected in Scenario 2 is shown in
Figure 16. In the case of heavy harmonic pollution in Scenario 2, the voltage distortion rate of multiple nodes in the system exceeds the limit in method 1. In method 2, to prevent node voltage distortion from exceeding the limit, an early warning signal is sent to the whole distributed system in advance, and each VDAPF in the whole network receives the operating position of other VDAPFs at the same time.
Figure 5,
Figure 6,
Figure 7,
Figure 8,
Figure 9,
Figure 10,
Figure 11,
Figure 12,
Figure 13,
Figure 14 show each node’s harmonic voltage mitigation results when the system weight coefficient
= 0.5; that is, the individual performance of the mitigation device is consistent with the proportion of the global mitigation effect. At this time, the voltage distortion of all nodes is below 4%, which proves the feasibility and superiority of method 2.
is set to 0.5 to meet the mitigation requirements of the distributed mitigation system.
Changing the weight coefficient of the system in the extreme case of
= 0 means that only the mitigation performance of the mitigation device is concerned, and the ideal mitigation effect cannot be obtained by providing a large compensation capacity, which does not meet the needs of the global mitigation effect and the system economy. When
= 1, only the global mitigation effect is considered, and the enthusiasm of mitigation devices to participate in mitigation is seriously reduced, which does not meet the needs of VDAPF self-organizing distributed optimization.
Figure 16 shows that when
= 0.5, the system’s harmonic mitigation demand is met. Next, a further discussion is provided on the influence of the harmonic distributed mitigation system as the weight coefficient
increases. After setting
= 0.8, the harmonic voltage distortion rate after mitigation is obtained for each grid node, as shown in
Figure 17.
Compared with the harmonic mitigation effect of each node when = 0.5, the harmonic distortion rate of each node decreases further when = 0.8, and the global harmonic voltage mitigation effect of the latter is better than that of the former. This shows that an appropriate increase in the value can reduce the comprehensive voltage distortion rate of the system and enhance the harmonic mitigation effect of the system. When is in the range of 0.9 to 1, the positive degree of the mitigation device decreases obviously with the increase in , and the total score of the mitigation effect also decreases. Similarly, other values of are verified. When 0.3 ≤ ≤ 0.9, the stability of the distributed mitigation system is better, and the higher requirements of the system on the harmonic distortion rate can be met by adjusting the value of = 0.8.
5.5. IEEE 69 Node Scalability Evaluation Arithmetic Analysis
In this study, the IEEE-69 bus system is used to verify the scalability and applicability of the proposed method further. The simulation example is used to evaluate the effectiveness of the proposed method for harmonic mitigation in larger-scale power systems with different topologies.
The IEEE-69 bus system is divided into six regions based on the integrated sensitivity partitioning method, including Region I–Region VI, as shown in
Figure 18. The mitigation nodes and observation nodes selected by the method in
Section 4 are listed in
Table 6.
Based on the partition results of the 69-bus system, six VDAPF harmonic mitigation devices are used to mitigate the harmonics in different regions synergistically. The parameters of the IEEE 69-bus system are consistent with those of the IEEE 33-bus system to verify the adaptability of the proposed method.
Figure 19 illustrates the compensation capacity changes in six mitigation devices with 200 training times in the IEEE 69-bus system experiment. During the training process, the compensation capacity
of each mitigation device increases by 0.002 S per training. The growth rate of the compensation capacity varies because of the different positivity values of each device. For example, mitigation device 5 participates in harmonic mitigation with the highest positivity, which is intuitively reflected in the largest growth slope. In addition, although the compensation capacity of device 6 is not the fastest growth, it can ultimately achieve and maintain a high compensation capacity, which is essential to ensure the stable operation of the power system under extreme conditions.
Table 7 demonstrates the residual compensation capacity of the devices under different nodes and their positivity to assess the performance and participation of each device. Among them, mitigation device 6 at node 27 has the largest residual compensation capacity of 18.0 A and a positivity factor
= 0.6. This implies that mitigation device 6 still has great potential in harmonic mitigation, and it is necessary to adjust strategies to improve the positivity of the mitigation device. In contrast, mitigation device 1 at node 50 shows sufficient residual capacity and the highest positivity, indicating that mitigation device 1 fully utilized its potential during the harmonic mitigation process and has satisfactory harmonic mitigation performance.
As shown in
Figure 20, when the compensation capacity of the mitigation devices is adjusted with the target of the required capacity of the neighboring regions, the mitigation integral of the device increases accordingly. At the 85th training, the mitigation integral of all the mitigation devices reached its peak. However, with the increase in the compensation capacity, the residual capacity of the self-region of the mitigation device may be insufficient, which will affect the effect of the whole area. This indicates that the mitigation integral strategy proposed in this paper can effectively control harmonic mitigation devices for the harmonic collaborative mitigation of the whole system.
After injecting the harmonic currents of Scenario 1, the total harmonic voltage distortion rates (
THDv) of the IEEE 69-bus system are mainly concentrated around 8%, as shown in
Figure 21. After the harmonic mitigation by the two methods, the
THDv of most nodes is significantly reduced to below 4.5%, indicating that both methods are effective in reducing harmonic pollution. Specifically, method 1 can reduce the
THDv of most regions, but there are still some nodes with high
THDv, such as nodes 16 and 17. On the other hand, method 2 can significantly reduce the
THDv of most nodes in all regions, indicating that method 2 has a better harmonic mitigation effect.
Figure 22 demonstrates the effectiveness of harmonic mitigation with the system weighting factor
under the condition of heavy harmonic pollution in Scenario 2. The analysis results show that the two methods can reduce harmonic pollution, but the mitigation effect of method 2 is better. In terms of details, the
THDv of method 2 is lower than that of method 1, and the performance is more significant, especially in Regions I, II, and III. However, the
THDv was not controlled within the safety threshold and still exceeded the limit of 4% regardless of the method. This study suggests that setting
fails to meet the mitigation needs of distributed mitigation systems in heavily harmonically polluted environments, and further exploration is needed to determine a more appropriate value of
.
The effect of increasing the weighting factor
on the harmonic distributed mitigation system is further discussed. The
THDv at each node after mitigation using
= 0.8 is shown in
Figure 23. Compared with the mitigation effect at
= 0.5, the
THDv of each node is lower with
= 0.8, and especially method 2 can effectively reduce the
THDv. This indicates that appropriately increasing the value of
can improve the positivity of the mitigation devices and the effect of harmonic mitigation of the whole system. Therefore, the weighting coefficients can be adjusted according to different operational requirements to achieve the harmonic mitigation of the system.
Through a comprehensive analysis of the IEEE 69-bus simulation experiment, the distributed mitigation method of six mitigation devices shows good applicability and effectiveness in larger-scale grid systems. The mitigation strategy of partition adjustment and regional mutual assistance significantly improves the harmonic mitigation effect, and the compensation capacity of each mitigation device is fully utilized to keep the THDv of the system at a low level.
5.6. Hardware Experiment
In order to enhance the reliability and scientific rigor of this study’s conclusions, this study also implemented hardware experiments and adopted the OPAL-RT system to examine the operational performance of the VDAPF. Specifically, the OPAL-RT system boasts high-precision and real-time simulation capabilities that enable detailed monitoring and analysis of the harmonics in the power grid, as shown in
Figure 24.
Firstly, the FFT spectrum of the VDAPF injection current was analyzed using the OPAL-RT system, as shown in
Figure 25. The spectrogram clearly shows the major harmonic frequency components, where distinct high-frequency noise indicates the presence of harmonic pollution problems in the grid. By analyzing these high-frequency components, the specific harmonic frequencies that require mitigation can be precisely identified. This allows the VDAPF to tailor its intervention, generating equal-amplitude reverse harmonic currents for effective harmonic mitigation.
Secondly, the compensation current injected by the VDAPF was studied in detail, as shown in
Figure 26. The waveforms and amplitudes of the compensation currents were analyzed to evaluate the compensation capability of the VDAPF under different load conditions.
Finally, the voltage waveforms after VDAPF mitigation were observed and recorded, as shown in
Figure 27. By comparing the voltage waveforms before and after mitigation, the effectiveness of VDAPF in improving power quality was evaluated. The results show that the voltage waveforms after VDAPF mitigation are smoother and close to the ideal sinusoidal waveforms. Additionally, the significant reduction in harmonic content confirms the VDAPF is effective in reducing harmonics in the power grid.
In summary, this study comprehensively and meticulously analyzes the injected currents and treated voltage waveforms of the VDAPF by means of the OPAL-RT system. Combined with simulation and experimental data, the important role of VDAPFs in harmonic mitigation and power quality improvement is shown. This study further validates the effectiveness and adaptability of the strategy of harmonic mitigation in this paper.