**5. Use Case Study**

To validate the presented voltage compensation algorithm, the longest branch of the IEEE 37 Node Test feeder [22] from Node 701–Node 741 was selected to simulate a mid-level distribution feeder branch with commercial loads. The transmission voltage level of 230 kV is transformed in distribution substation to 4.8 kV in the feeder. Different combinations of commercial building load profiles obtained from [23] were used as uncontrollable load of microgrids connected to each node. In addition to building loads, microgrids on node 702, 730, 708, 734, 738 and 741 had PEV chargers. Figure 5 shows the distribution grid topology of the use case. The building loads and the number of EVSEs under each node are listed in Table 1. A total of 120 EVSEs were installed in six microgrids to charge three types of PEVs. The PEV battery and charging parameters are listed in Table 2. The power factors of the building load and PEV charger were 0.95 and 0.98, respectively.

**Figure 5.** The distribution grid topology in the use case study.


**Table 1.** The building and number of EVSEs in microgrids.

**Table 2.** PEV battery and charging parameters [17].


We simulated the voltage compensation at 10:00 am and assumed that all the EVSEs were connected with PEVs. This resulted in 120 PEVs (31 Nissan Leaf 2013s, 20 BMW i3 2014s, and 69 Chevy Volt 2013s) in the simulation. These PEVs were randomly allocated to EVSEs. The initial and target SOCs of the PEVs were also randomly generated. Table 3 shows the uncontrollable load and maximal PEV charging power demand at 10:00 am. The variation and effect from other feeder branches are not considered. In addition, it was assumed that the grid was balanced, and the node loads were all connected to the same phase on the feeder branch.

One distribution voltage violation was simulated at Node 741 with 0.933 per unit when all microgrids chose to charge PEVs at maximum charging power. After all microgrids curtailed PEV charging power to critical point, the voltage violation still existed at Node 741 with 0.948 per unit. In this situation, a negotiation among the grid-level agent and microgrid agents to further curtail PEV charging power for the voltage compensation is triggered. Firstly, the voltage–load variation relationship coefficients were found to be coef = [0.2396, 0.4420, 0.7242, 1.0718, 1.1869, 1.3710, 1.5548, 1.8788, 2.2462, 2.4738, 2.6975, 2.9188], which were used as the grid voltage compensation reference. Each VGI microgrid wishes to retain a charging power close to its PEV critical charging power point. On the other hand, the grid-level agent wishes to compensate the voltage at Node 741 back to 0.9505 per unit. The negotiation process is shown in Figure 4.


**Table 3.** Uncontrollable load and PEV charging power demand at 10:00 am in each node along the distribution feeder branch.

Figures 6 and 7 show the selection of negotiation parameters, such as the penalty factor ρ and the proximal factor φ, and their effects on the residual convergence. It is shown in Figure 6 that a larger penalty factor ρ can accelerate the negotiation. However, the negotiation oscillates when the penalty factor exceeds a certain value. The introduction of a proximal term helps to improve the convergence of the negotiation process. Figure 7 shows simulation results for different values of the proximal factor φ when the penalty factor ρ = 0.2. It is observed that the proximal term enhances the possibility of convergence of the negotiation. However, an excessively large proximal factor results in divergence. After a number of simulations, an empirical conclusion was that it is relatively safe to choose a penalty factor that is smaller than 1 and a proximal factor that is 5–10 times larger than the penalty factor.

With the penalty factor, ρ = 0.2 and the proximal factor, φ = 1, the negotiation shows a fast convergence speed within 30 rounds. Figure 8 shows the update sequence of the microgrid power curtailment and the grid level-agent decisions in the negotiation process. The negotiation finally reaches an agreement that the VGI microgrids' charging power curtailments are 2.44k W (node 702), 5.37 kW (node 730), 6.79 kW (node 708), 9.19 kW (node 734), 12.02 kW (node 738), and 14.16 kW (node 741) from their critical charging points. On the other hand, the grid-level agent adjusts its Δ|V741| 2 requirement from 109.35 <sup>×</sup> <sup>10</sup><sup>3</sup> to 104.49 <sup>×</sup> 103.

**Figure 6.** The negotiation process with different values of penalty factor ρ. Sub-figure (**a**) shows a very slow convergence rate with ρ = 0.01, Sub-figure (**b**,**c**) show faster convergence within the range 0.05 ≤ ρ ≤ 0.1, but (**c**) demonstrates an even better convergence rate. Sub-figure (**d**) show negotiation does not converge when ρ increases and reaches 0.2.

**Figure 7.** The negotiation process with different values of proximal factor φ. Adding proper proximal factor can increase the robustness of the negotiation. Sub-figure (**a**) shows adding a small Proximal Factor, φ = 0.2, does not help negotiation with a large penalty factor ρ = 0.2 to converge. Sub-figure (**b**,**c**) show that if the proximal factor, φ, is within proper range, the robustness of negotiation increases. (**d**) demonstrates an exceedingly large proximal factor, φ, breaks the negotiation convergence.

**Figure 8.** Updates of microgrid power curtailment ΔPCap,k and the voltage square variation Δ|V741| 2 during negotiation. (**a**) shows the power capacity curtailment evolvements of different VGI Microgrids along the distribution line during the negotiation process. (**b**) shows the voltage square difference caused by change of VGI Microgrids power capacity change during the negotiation process.

Figure 9 shows the PEV charging power and CoC comparison in each microgrid before and after the voltage compensation negotiation. The charging power of some PEVs is further reduced and results in the CoC value falling below zero. It was also found that VGI microgrids that are close to the voltage violation node curtail more power than the VGI microgrids that are far away from the voltage violation node. The reason is that the load variation near the voltage violation node has a larger effect on the voltage regulation.

**Figure 9.** The negotiation effects on PEV charging in the microgrids. (**a**–**f**) show PEV Charging power and CoC value comparison before and after the negotiation process in different VGI Microgrids along the distribution lines.

The simulation result testifies to the effectiveness of the distribution voltage compensation. Figure 10 shows the distribution voltage of each node along the distribution feeder line. The comparison is shown for the PEV charging scenarios: maximal power demand charging, charging at the VGI microgrid PEV critical charging power point, and charging after voltage compensation negotiation. The voltage compensation negotiation successfully raises the Node 741 voltage to around 0.9504 per unit.

**Figure 10.** Voltage along the distribution feeder branch in different charging scenarios at 10:00 am.

### **6. Conclusions**

This paper presents a distributed VGI control to realize voltage compensation service in a distribution network. The control scheme design is composed of two levels–the microgrid level and the distribution grid level. At the top level—the distribution grid level—an ADMM-based distributed voltage compensation negotiation among the multiple VGI microgrid agents and a grid-level agent is triggered when a voltage violation occurs. This distribution grid agent aims to maintain its distribution voltage level above the lowest threshold by sacrificing the microgrids' power capacity. On the other side, each VGI microgrid agent wishes to minimize its power capacity curtailment to lower the impact to the PEV charging activities with in the VGI microgrid. Though having conflicting objectives, the negotiation coordinates the interests of all agents as an entity and finally reaches an agreement that all agents can accept. After determining the power capacity curtailment for each VGI microgrid, the CoC-based optimal microgrid VGI control algorithm aims to reasonably dispatch limited power to the charging PEVs and results in an average PEV charging satisfaction at the lower level, the VGI microgrid. We used a case study to simulate the application of the proposed algorithm in a VGI distribution grid to prove its effectiveness and advantages. First, the distributed algorithm allows each agent to pursue its own objective under the coordination of negotiation. This greatly reduces the computation burden of a single control unit compared to a centralized control design. Secondly, the two-level control design decouples the distribution grid-level control and single PEV charging control at the microgrid level. Each VGI microgrid becomes a relatively independent entity that controls the PEV charging activities within its range. This organization increases the scalability of the control scheme. However, the scenario presented in this paper applies certain simplifications. For example, distributed generation, like from renewable energy sources, was not considered. The possible utilization of a four-quadrant power inverter and large energy storage were also not in consideration. All these factors may provide both additional flexibility and uncertainty for the VGI control design in the distribution grid. We are going to consider improving the proposed control algorithm to better adapt to the factors above in future study.

**Author Contributions:** Conceptualization, C.C., Z.W. and B.C.; Methodology, C.C., Z.W. and B.C.; Software, C.C.; Validation, C.C.; Formal Analysis, C.C.; Investigation, C.C.; Resources, C.C.; Data curation, C.C.; Writing—original draft preparation, C.C.; Writing—review and editing, C.C. and B.C.; Visualization, C.C.; Supervision, B.C.; Project administration, B.C.; Funding acquisition, B.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
