Bi-level Volt/VAR Optimization in Distribution Networks with Smart PV Inverters

Abstract: Optimal Volt/VAR control (VVC) in distribution networks relies on an effective coordination between the conventional utility-owned mechanical devices and the smart residential photovoltaic (PV) inverters. Typically, a central controller carries out a periodic optimization and sends setpoints to the local controller of each device. However, instead of tracking centrally dispatched setpoints, smart PV inverters can cooperate on a much faster timescale to reach optimality within a PV inverter group. To accommodate such PV inverter groups in the VVC architecture, this paper proposes a bi-level optimization framework. The upper-level determines the setpoints of the mechanical devices to minimize the network active power losses, while the lower-level represents the coordinated actions that the inverters take for their own objectives. The interactions between these two levels are captured in the bi-level optimization, which is solved using the Karush-Kuhn-Tucker (KKT) conditions. This framework fully exploits the capabilities of the different types of voltage regulation devices and enables them to cooperatively optimize their goals. Case studies on typical distribution networks with field-recorded data demonstrate the effectiveness and advantages of the proposed approach.

• The paper introduces a bi-level optimization framework that coordinates traditional devices and smart PV inverters to minimize network active power losses.
• It employs an upper-level MISOCP for scheduling OLTCs and capacitor banks and a lower-level distributed control for real-time inverter adjustments.
• Simulation on the IEEE 33-bus network demonstrates a 15.7% reduction in daily power losses and improved voltage regulation compared to conventional methods.

Bi-level Volt/VAR Optimization in Distribution Networks with Smart PV Inverters

This paper introduces a bi-level optimization framework designed to enhance Volt/VAR Control (VVC) in distribution networks, particularly in scenarios with high penetration of smart residential photovoltaic (PV) inverters. Traditional mechanical devices such as on-load tap changers (OLTCs) and capacitor banks (CBs) are complemented and coordinated with the rapid-response capabilities of smart PV inverters, allowing for improved voltage regulation and reduced network losses.

Framework Overview

The bi-level optimization model is structured into two distinct levels:

1. Upper-Level Optimization: This level is responsible for scheduling conventional mechanical devices with the aim of minimizing network active power losses. It is formulated as a Mixed Integer Second Order Cone Programming (MISOCP) problem, incorporating constraints that reflect PV inverter reactive outputs based on Karush-Kuhn-Tucker (KKT) conditions.
2. Lower-Level Optimization: It models the fast, autonomous actions of smart PV inverters, which adjust their reactive outputs to resolve sudden voltage deviations and optimize their own objectives, such as minimizing reactive power costs or equalizing the inverter utilization ratios. This process is executed in a distributed manner, leveraging local measurements and communication among inverters.

   Figure 1: Overview of the implementation of the bi-level optimization model.

Implementation Details

Upper-Level Optimization

The upper-level dispatches OLTCs and CBs using a periodic schedule to minimize active power losses and maintain network stability. The optimization involves:

• Utilizing the DistFlow model to accurately represent power flows.
• Relaxing nonconvex constraints with second-order cone programming to ensure computational feasibility.
• Coordinating the network voltage profiles by setting tap positions on OLTCs and controlling CB units.

Lower-Level Optimization

Smart PV inverters operate autonomously within the scope defined by the upper-level. They iteratively adjust their reactive power outputs by solving a local optimization problem. Key elements include:

• Real-time adjustments based on local voltage measurements.
• Communication with neighboring inverters to enhance cooperative behavior.
• Achieving convergence to optimal reactive power outputs through distributed control algorithms.

  Figure 2: PV inverter reactive output iteration process at 13:00.

Case Study Analysis

Simulation results from standard IEEE test feeders illustrate the effectiveness of the bi-level optimization approach. With regards to the IEEE 33-bus network:

• The average daily active power losses were reduced by approximately 15.7% compared to scenarios without optimized control.
• The combined actions of OLTCs, CBs, and smart PV inverters successfully maintained voltage levels within predefined limits throughout fluctuating load conditions.

  Figure 3: Network voltage profiles without any control.

  

  Figure 4: Network voltage profiles with the proposed control.

Comparison with Traditional Models

The bi-level model demonstrates superior performance compared to single-level optimization models that either directly control PV inverter outputs or neglect their contributions altogether. Comparative analysis shows:

• The solution time increases with bi-level models due to additional complexity, yet the reduction in active power losses substantiates its efficacy.
• Traditional models fail to harness the full reactive capabilities of smart PV inverters, leading to suboptimal loss minimization.

Conclusion

The bi-level optimization framework presents a significant advancement in integrating smart PV inverters into the VVC architecture, enabling both system-wide coordination and swift local response to voltage fluctuations. Future research should focus on extending this framework to three-phase unbalanced networks and incorporating additional types of voltage regulation resources, such as active power control from PV inverters. This approach provides a robust and flexible solution for modern distribution networks challenged by high renewable energy penetration.