⚡ electrical engineering

Optimal Loss Reduction in Distribution Networks Using Conservation Voltage Reduction and Network Topology Reconfiguration

This paper proposes a coordinated day-ahead optimization framework that integrates Conservation Voltage Reduction (CVR) and Network Topology Reconfiguration (NTR) into a mixed-integer conic programming model, demonstrating through IEEE 33 and 123-bus system tests that this coupled approach reduces active power losses by up to 20.6% while outperforming independent strategies.

Original authors: Rida Fatima, Hassan Zahid Butt, Xingpeng Li

Published 2026-05-12

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rida Fatima, Hassan Zahid Butt, Xingpeng Li

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the electrical grid that powers our homes and businesses as a massive, complex system of water pipes. The goal of the utility company is to get water (electricity) from the main reservoir (the substation) to every faucet (your home) with as little waste as possible.

This paper proposes a new way to manage that system by combining two existing strategies into one "super-team" approach. Here is how the authors explain it using simple concepts and analogies.

The Two Old Strategies (The Solo Players)

For a long time, engineers have used two separate tricks to stop energy waste (which happens when electricity fights against the resistance of the wires, creating heat):

The "Turn Down the Tap" Strategy (CVR):
- The Idea: Most things we plug in (like lights and heaters) use less electricity if the voltage (water pressure) is slightly lower.
- The Analogy: Imagine you have a garden hose. If you turn the pressure down just a tiny bit, the water still reaches the plants, but you use less water overall. In the paper, this is called Conservation Voltage Reduction (CVR). It's like gently turning down the pressure on the main valve so the whole neighborhood uses slightly less power without anyone noticing a difference in their lights.
- The Catch: If you turn the pressure down too much, the water at the end of the hose (the furthest houses) might not flow at all.
The "Rearrange the Pipes" Strategy (NTR):
- The Idea: Sometimes, electricity has to travel a long, winding route to get to a house, which causes more waste.
- The Analogy: Imagine a traffic jam on a highway. Instead of forcing everyone to stay in the same lane, you open a new exit ramp and close a blocked road to create a shorter, smoother path. In the paper, this is called Network Topology Reconfiguration (NTR). It involves flipping switches to change the physical path electricity takes, finding the shortest, most efficient route to every home.
- The Catch: Just rearranging the pipes doesn't change how much water the faucets are demanding.

The Problem: They Were Playing Alone

The authors point out that in the past, engineers treated these two strategies as separate jobs. They would either turn down the pressure or rearrange the pipes, but rarely both at the same time.

The Analogy: It's like trying to fix a traffic jam by only changing the speed limit, or only changing the road layout, but never doing both together. The paper argues that these two strategies actually help each other.

If you turn down the pressure (CVR), the pipes carry less water, which makes it easier to rearrange the pipes (NTR) without causing bottlenecks.
If you rearrange the pipes (NTR) to be more efficient, the pressure drops less along the way, which allows you to turn the pressure down even further (CVR) safely.

The New Solution: The "Coordinated Team"

The paper proposes a Unified Optimization Framework. Think of this as a smart, central brain that looks at the whole neighborhood at once and says, "Okay, let's turn down the pressure just enough to save energy, and at the same time, let's flip these specific switches to reroute the power through the best possible paths."

They built a mathematical model (a complex set of rules for a computer) that considers:

The Load: How much power people are using.
The Solar Panels: New energy sources that change how much power is available during the day.
Batteries: Storage that can charge or discharge to help balance things out.
The Physics: Ensuring the voltage doesn't get too low (lights dimming) or too high (equipment breaking).

What They Found (The Results)

The authors tested this "Team Approach" on two famous test models of electrical grids (the IEEE 33-bus and IEEE 123-bus systems). Think of these as digital simulations of real neighborhoods.

The Solo Players:
- Just rearranging the pipes (NTR) saved some energy.
- Just turning down the pressure (CVR) saved some energy.
The Team Approach (CVR + NTR):
- When they worked together, the results were much better than the sum of their parts.
- On the larger test system, the combined approach reduced wasted energy (active power losses) by 20.6% compared to doing nothing.
- It also made the flow of electricity more even across the whole network, preventing any single wire from getting "overworked" or overheated.

The Bottom Line

The paper concludes that by treating voltage control and network switching as a single, coordinated job rather than two separate tasks, we can make our power grids significantly more efficient. It's a way to get more power to our homes with less waste, simply by having the system "think" about both the pressure and the path at the same time.

Technical Summary: Coordinated Optimization of CVR and NTR in Distribution Networks

Problem Statement
Distribution networks (DNs) are increasingly challenged by rising demand, extended feeder lengths, and the high penetration of distributed energy resources (DERs), which introduce significant variability in power injections. While Conservation Voltage Reduction (CVR) and Network Topology Reconfiguration (NTR) are established methods for improving system performance, existing literature largely treats them as independent strategies. This separation overlooks their coupled physical impact: CVR alters nodal voltages and load demand, which in turn affects power flow distribution and optimal feeder configuration; conversely, NTR changes network connectivity and branch impedances, influencing voltage profiles and the efficacy of voltage reduction. This lack of coordination limits the overall effectiveness of loss reduction and voltage regulation efforts.

Methodology
The authors propose a unified, day-ahead operational planning framework that jointly optimizes CVR and NTR within a radial distribution network. The core of the methodology is a Mixed-Integer Conic Programming (MICP) model that incorporates:

AC Power Flow Constraints: The model uses a branch-flow formulation with conic relaxation (squaring voltage and current magnitudes) to handle nonlinearities while ensuring computational tractability.
Voltage-Dependent Load Modeling: Loads are represented using ZIP (Constant Impedance, Constant Current, Constant Power) models to accurately capture how demand varies with voltage, a critical factor for CVR effectiveness.
Network Topology Reconfiguration (NTR): Binary decision variables determine the open/closed status of flexible branches. Radiality constraints ensure the resulting topology remains loop-free.
Conservation Voltage Reduction (CVR): Implemented by tightening the lower bound of allowable nodal voltages via a reduction factor ( $\vartheta$ ), allowing the optimizer to systematically reduce voltages to lower load demand and losses.
Resource Integration: The framework explicitly models the operation of Photovoltaic (PV) systems, Battery Energy Storage Systems (BESS), and dispatchable generators, including curtailment constraints and state-of-charge dynamics.

The problem is solved using the Pyomo modeling framework and the Gurobi optimizer, utilizing a branch-and-bound strategy for binary variables and second-order conic constraints for power flow relationships.

Key Contributions

Unified Framework: The paper develops a single optimization model that simultaneously adjusts voltage levels and network topology, capturing the synergistic interaction between load reduction (via CVR) and power flow redistribution (via NTR).
Integrated Modeling: It integrates AC power flow, ZIP load characteristics, and DER operations into a conic programming structure, moving beyond simplified linearized models or constant-power load assumptions often found in independent studies.
Comparative Analysis: The study rigorously evaluates four distinct scenarios: Standard DN (SDN), Reconfigured DN (SDNTR), CVR-enabled DN (CEDN), and the coordinated CVR-NTR (CEDNTR) across different load models (CI, CC, CP) and with/without DERs.

Results
The framework was validated on the IEEE 33-bus and IEEE 123-bus distribution systems under hourly load variations.

IEEE 33-bus System: The coordinated approach (CEDNTR) consistently outperformed independent strategies. While NTR alone reduced losses by ~7–10% and CVR showed significant gains under impedance-dependent loads, the combined approach achieved the lowest active power losses. The optimal switching patterns remained largely consistent across configurations, suggesting that structural optimization is the primary driver, with CVR providing secondary benefits.
IEEE 123-bus System: In this larger, more complex system, the base case (SDN) exhibited approximately 17 kW of active power losses.
- NTR alone reduced losses by ~5.9%.
- CVR alone reduced losses by ~12.9%.
- Coordinated CVR-NTR achieved a 20.6% reduction in active power losses (down to ~13.5 kW), demonstrating a synergistic effect greater than the sum of individual strategies.
Branch Loading: The coordinated approach significantly improved branch loading uniformity, reducing the maximum line loading from ~75% (SDN) to ~62% (CEDNTR), thereby alleviating localized congestion.
Load Model Sensitivity: The results confirmed that CVR effectiveness is highly dependent on load voltage sensitivity (strongest in Constant Impedance models) and is further enhanced by the presence of DERs.

Significance and Claims
The paper claims that the coordinated optimization of CVR and NTR provides a scalable and effective solution for enhancing efficiency in modern distribution networks. The authors assert that the inherent coupling between voltage control and network topology means that treating these strategies independently yields suboptimal results. By jointly optimizing these mechanisms, the framework achieves superior loss reduction, improved voltage compliance, and more uniform branch loading compared to conventional independent implementations. The study concludes that this integrated approach is robust and applicable to large-scale networks, offering a practical pathway for day-ahead operational planning in systems with high DER penetration.