PaperlayerView exact revision on arXiv

Source-linked AI summary

Coordinated Conservation Voltage Reduction and Network Topology Reconfiguration in Active Distribution Networks

Rida Fatima, Hassan Zahid Butt, Xingpeng Li

arXiv:2610.17122v1eess.SYcs.SY

TL;DR

CVR and NTR are often optimized independently despite their coupled effects on feeder voltages, demand, flows, and losses. This paper jointly optimizes feeder-head voltage control and network reconfiguration in a day-ahead MISOCP. Across the reported feeder studies, their benefits are complementary and depend on operating conditions.

  • Problem

    CVR and NTR are commonly optimized independently even though each changes conditions relevant to the other, potentially missing operating points created by their interaction.

    Source: §1 · p. 3

  • Method

    A day-ahead MISOCP jointly optimizes feeder-head voltage setpoints and binary reconfiguration while incorporating ZIP loads, DER scheduling, BESS operation, and multi-substation radiality.

    Source: §2 · p. 5

  • Results

    Coordinated CVR and NTR provide complementary, condition-dependent benefits, including 17.65% active energy loss reduction relative to SDN under constant impedance loading and feasibility at 120% loading when SDN is infeasible.

    Source: §5 · pp. 19–20, §4.3 · p. 19

  • Takeaways & Limitations

    The reported benefits vary with load composition, DER scaling, feeder topology, voltage margins, and source capacity constraints.

    Source: §5 · pp. 19–20

    Feeder-head voltage control is modeled as continuous; discrete tap positions and detailed OLTC or regulator logic are not represented.

    Source: §2.11 · p. 10

Abstract

from arXiv · show

Distribution networks rely on conservation voltage reduction (CVR) and network topology reconfiguration (NTR) to manage demand, distributed energy resources (DERs), and tighter operating margins. Yet these strategies are typically deployed independently, despite coupled effects on feeder voltages, losses, and loading. This paper addresses that gap by developing a day-ahead mixed-integer second order cone programming (MISOCP) framework that jointly optimizes feeder head voltage control and network reconfiguration. The formulation incorporates AC branch flow constraints, ZIP load models, DERs, battery energy storage systems, and multi substation radiality. Using modified IEEE 33 bus and 123 bus systems, four configurations isolate the individual and coordinated effects of CVR and NTR. On the 33-bus system under mixed ZIP loading, NTR reduces active energy loss by 2.50%, while coordinated operation reduces it by 2.91% relative to SDN and produces a 2.46% CVR induced active load reduction relative to SDNTR. Under constant impedance loading, coordinated operation reduces active energy loss by 17.65% relative to SDN, while CVR reduces active load by 14.61% relative to SDNTR. DER portfolio scaling shows a nonmonotonic coordinated load reduction response, strongest at 20% penetration and decreasing at higher levels. On the 123 bus system, NTR reduces losses by 19.3%, while CVR reduces voltage dependent load energy by 2.3 to 2.4%. Under loading stress, SDN becomes infeasible at 120% loading, whereas CEDNTR remains feasible. Overall, the results demonstrate complementary, operating condition dependent benefits shaped by load composition, DER portfolio scaling, feeder topology, voltage margins, and source constraints, highlighting the value of joint optimization.

Nomenclature

The nomenclature defines the sets, indices, parameters, and decision variables used to describe the network, resources, operating limits, and scheduling horizon.

Sets and Indices

  • Network sets and indices identify substations, nodes, branches, switchable branches, scheduling intervals, generators, PV units, and batteries.The notation also distinguishes incoming and outgoing branches and indexes each device and time interval.Source: Nomenclature · pp. 1–2

Parameters

  • Parameters specify nominal demands, feeder-head and nodal voltage bounds, branch impedances and current limits, substation supply limits, and switching limits.They also include ZIP load coefficients, PV availability, battery operating limits, and initial branch status.Source: Nomenclature · p. 2

Variables

  • Decision variables represent branch status and flows, node voltage and branch current magnitudes, resource dispatch, battery operation, and auxiliary connectivity flows.The notation includes voltage-dependent active and reactive ZIP demand and conic-relaxation residuals.Source: Nomenclature · pp. 2–3

1. Introduction

The introduction motivates coordinating CVR and NTR because they affect demand, voltage profiles, and power flows through interacting mechanisms. It positions a unified MISOCP framework to evaluate those interactions across operating conditions.

1. Introduction

  • Rising demand, longer feeders, and growing DER penetration increase operational stress, while CVR and NTR offer distinct ways to influence demand, losses, and loading.The introduction notes that high DER penetration can create overvoltage and complicate power-flow management.Source: §1 · p. 3

1.1 Network Topology Reconfiguration

  • NTR changes sectionalizing and tie-switch states to redistribute flows; conic branch-flow models underpin tractable reconfiguration optimization.Prior work also extends NTR to varied objectives, but often optimizes topology or resource operation separately from voltage reduction and demand response.Source: §1.1 · pp. 3–4

1.2 Conservation Voltage Reduction

  • CVR operates feeder voltage near the allowable lower range, with effectiveness depending on voltage-sensitive load composition represented by ZIP components.The ZIP representation links feeder-head voltage reductions to changes in nodal demand, flows, and losses.Source: §1.2 · p. 4

1.3 Coordinated CVR and NTR: Research Gap and Positioning

  • Because CVR changes demand and NTR reshapes feeder paths, optimizing them separately can miss operating points created by their interaction.The paper positions joint optimization of feeder-head voltage setpoints and binary reconfiguration, with DERs, BESSs, ZIP loads, and multi-substation radiality.Source: §1.3 · pp. 4–5

1.4 Contributions

  • The contributions include a controlled comparison of four configurations and sensitivity analyses across ZIP composition, DER scaling, and feeder size.The IEEE 123-bus study examines scalability and loading robustness; the IEEE 33-bus study reports up to 17.65% loss reduction and 14.61% CVR-induced active-load reduction under constant impedance loading.Source: §1.4 · p. 5

2. Network Modeling & Optimization Formulation

The formulation minimizes daily active energy losses using a MISOCP branch-flow model that combines network operation, voltage-dependent loads, and resource decisions. Its constraints represent power balance, switching-dependent voltage coupling, and a conic relaxation of the voltage-current-power relationship.

2. Network Modeling & Optimization Formulation

  • The MISOCP minimizes active energy losses over 24 hours while jointly optimizing feeder-head voltage, reconfiguration, and DER operation under network and switching constraints.The model includes AC branch flows, ZIP demand, BESS scheduling, multi-substation radiality, voltage and thermal limits.Source: §2 · p. 5

2.1 Auxiliary Variable Definitions

  • Squared nodal voltage and branch current variables support a conic-compatible branch-flow formulation and avoid explicit square-root expressions.Squared voltage is also used in the constant-impedance load term; the constant-current term uses a linear voltage-magnitude approximation.Source: §2.1 · pp. 5–6

2.2 Objective function

  • The objective sums branch active-power losses over the 24-hour horizon, equivalent to daily active energy loss because each interval lasts one hour.The objective minimizes network losses rather than supplied energy or customer demand, so load reduction is an outcome rather than a direct target.Source: §2.2 · p. 6

2.3 Power Flow and Network Constraints

  • Nodal active and reactive power balances equate net injections to incoming and outgoing flows, adjusted for branch losses.These constraints apply at every scheduling interval.Source: §2.3 · p. 6
  • The switch-dependent voltage-drop constraint enforces the branch-flow voltage equation when a branch is closed and relaxes voltage coupling when it is open.This permits topology changes without imposing a voltage relation across disconnected branches.Source: §2.3 · p. 6
  • A second-order cone relaxation represents the nonlinear voltage-current-power relationship while coupling active and reactive flows, squared current, and sending-end squared voltage.Relaxation tightness is checked after optimization using residual metrics.Source: §2.3 · pp. 6–7

2.4 Nodal Power Injection Modeling

Nodal injections combine network supply and resource decisions with voltage-dependent demand, linking DER operation and load modeling to power balance.

2.4 Nodal Power Injection Modeling

  • Nodal active and reactive injections combine substation supply, curtailed PV generation, BESS charging and discharging, dispatchable generation, and voltage-dependent load.These resource decisions directly affect the nodal power-balance constraints and resulting network flows.Source: §2.4 · p. 7

2.5 Voltage-Dependent Load Modeling

  • The ZIP model represents active and reactive demand using constant-impedance, constant-current, and constant-power components.The impedance component varies with squared voltage, the power component is voltage-independent, and the current component uses a first-order approximation around nominal voltage.Source: §2.5 · p. 7

2.6 Operational Constraints

Network, PV, and storage constraints keep the day-ahead schedule within operating limits while allowing physically valid generation and storage decisions.

2.6 Operational Constraints

  • Constraints (12)–(19) enforce nodal voltage and branch thermal limits, couple branch flows and currents to switch status, and bound generator and substation injections.Substation limits define the feeder-head capacity boundary for each feeder region.Source: §2.6 · pp. 7–8

2.7 Photovoltaic Curtailment Constraints

  • PV curtailment is bounded by available generation, and actual PV injection equals available generation minus curtailed power.These constraints keep curtailment physically valid and prevent PV output from exceeding available resources.Source: §2.7 · p. 8

2.8 Energy Storage System Modeling

  • BESS constraints enforce state-of-charge and power limits, mutually exclusive charging and discharging, and intertemporal energy balance.Stored energy returns to its initial value at the end of the 24-hour horizon, preventing net depletion.Source: §2.8 · p. 8

2.9 Network Topology Reconfiguration

Binary branch statuses let the optimizer change switchable branches while preserving a radial, substation-connected network and limiting switching activity.

2.9 Network Topology Reconfiguration

  • Binary branch status indicates whether a branch is open or closed; only switchable branches may change status, and open branches carry no current or power.Branch current, power-flow, and voltage-drop constraints are linked to status so the selected topology remains physically consistent.Source: §2.9 · pp. 8–9

2.10 Multi-Substation Radiality

  • Each interval’s energized network must form a radial forest rooted at substations, with every energized component connected to exactly one substation.Auxiliary connectivity flows and branch-count constraints enforce the multi-substation radiality condition.Source: §2.10 · p. 9
  • NTR-enabled cases allow four switching actions, and the model imposes no terminal-topology constraint.The switching budget counts branch-status changes over the scheduling horizon.Source: §2.10 · p. 9

2.11 Conservation Voltage Reduction

CVR acts through feeder-head voltage control, reducing voltage-dependent demand while keeping nodal voltages within limits.

2.11 Conservation Voltage Reduction

  • With CVR disabled, the substation voltage is fixed at its prescribed base value.With CVR enabled, feeder-head voltage is optimized continuously within its allowable range.Source: §2.11 · p. 9
  • Lower feeder-head voltage decreases the voltage-dependent portions of active and reactive demand through the ZIP load model.The setpoint is optimized jointly with DER dispatch, BESS operation, and network topology, subject to nodal voltage limits.Source: §2.11 · p. 10
  • The model assumes continuous feeder-head voltage control and does not explicitly represent discrete tap positions or detailed OLTC or regulator logic.Source: §2.11 · p. 10

2.12 Coordinated Optimization Framework

The framework jointly schedules voltage control, network topology, and distributed resources to minimize active energy losses. It is solved and checked across a 24-hour horizon, with evaluation scenarios comparing the individual and coordinated effects of CVR and NTR.

2.12 Coordinated Optimization Framework

  • The day-ahead MISOCP jointly optimizes topology, feeder-head voltage setpoints, substation injections, DER dispatch, PV curtailment, and BESS operation to minimize total active energy losses.The formulation includes branch-flow and ZIP demand models, operating limits, multi-substation radiality, and a switching budget.Source: §2.12 · p. 10

2.13 Solution Strategy and Post-Solution Validation

  • The complete 24-hour horizon is optimized simultaneously at one-hour resolution, and post-solution checks verify topology, power balance, voltage limits, and conic-relaxation tightness.Small residuals indicate that the relaxed solution closely satisfies the original nonlinear voltage–current–power relationship.Source: §2.13 · p. 10

2.14 Evaluation Scenarios and Performance Metrics

  • Four configurations use identical network data, profiles, operating limits, BESS assumptions, and scheduling conditions, differing only in whether CVR and NTR are enabled.Comparisons include active energy loss, active load energy, minimum nodal voltage, switching activity, and inter-substation load transfer; Table 1 summarizes the configurations.Source: §2.14 · pp. 10–11, Table 1 · p. 11

3. Case Study and Performance Evaluation

The 24-hour case studies compare fixed-topology and reconfigured operation, with and without CVR, on a modified IEEE 33-bus network. Coordinated operation gives the largest mixed-ZIP loss reduction, while its load-reduction benefit varies with ZIP composition and DER scaling.

3.1 Modified IEEE 33-Bus Network Configuration

  • The 33-bus study uses two substation-rooted radial regions, 35 candidate branches, and a jointly optimized one-hour-resolution schedule over 24 hours.The system includes PV, BESSs, and dispatchable generators; feeder-head voltage setpoints are optimized when CVR is enabled.Source: §3.1 · pp. 11–12

3.2 Base Case Comparative Assessment

  • 2.91% active energy loss reduction for CEDNTR and 2.50% for SDNTR, both relative to SDN, under the representative mixed ZIP case.CEDNTR achieves the lowest loss among the four configurations.Source: Figure 3 · p. 12, §3.2 · p. 12
  • CEDNTR lowers mean voltage to 1.0163 p.u. from about 1.0401 p.u. in CEDN and reduces active load by 2.46% relative to SDNTR.The minimum voltage reaches 0.9500 p.u.; CEDNTR reduces average active load from 2.193 MW to 2.140 MW and average active loss from 0.0172 MW to 0.0167 MW.Source: §3.2 · p. 12, Figure 4 · p. 13, §3.3 · p. 13

3.4 Sensitivity to ZIP Load Composition

  • 17.65% active energy loss reduction relative to SDN under constant-impedance loading; coordinated loss reduction rises as the constant-impedance share increases.For CEDNTR, loss reduction is 4.93% at 40%, 9.39% at 60%, and 13.72% at 80% constant-impedance share.Source: Figure 6 · p. 14, §3.4 · pp. 14–15
  • With NTR, active load reduction rises from 2.46% under mixed ZIP loading to 14.61% at 100% constant-impedance share; without NTR, it rises from 0.01% to 14.36%.Increasing voltage sensitivity makes CVR more effective even with fixed topology, reducing NTR's relative contribution to demand reduction.Source: Figure 7 · p. 15, §3.4 · p. 15
  • Under constant-power loading, CVR yields zero active load reduction; under constant-current loading, reductions are 7.19% without NTR and 6.28% with NTR.For constant-current loading, CEDN and CEDNTR reduce losses by 1.22% and 3.52%, respectively.Source: §3.4 · p. 15, Table 3 · p. 15

3.5 Sensitivity to DER Portfolio Scaling

  • CEDNTR's active energy loss reductions relative to SDN are 2.51%, 2.91%, 2.01%, and 2.70% at 0%, 20%, 40%, and 80% DER scaling, respectively.CEDNTR has the lowest normalized loss ratio at each evaluated level.Source: Figure 8 · p. 16, §3.5 · p. 16
  • CEDNTR's active load reduction relative to SDN peaks at 2.45% with 20% DER scaling, then falls to 2.07% at 40% and 0.16% at 80%.The reduction is negligible at 0%; at 80%, higher mean voltage reduces achievable voltage-dependent demand reduction.Source: Figure 9 · p. 16, §3.5 · p. 16

4. Scalability and Loading Robustness on the IEEE 123 Bus System

The modified IEEE 123-bus study evaluates the framework’s scalability and operating performance across four configurations, computational checks, and loading stress. NTR dominates loss reduction under the tested ZIP mix, while coordinated operation supports higher tested loading than SDN.

4. Scalability and Loading Robustness on the IEEE 123 Bus System

  • The study tests a balanced equivalent of the modified IEEE 123-bus feeder with the same 24-hour horizon, mixed ZIP model, voltage limits, and DER assumptions as the 33-bus study.The larger optimization has approximately 27,288 variables, including 3,168 binary variables.Source: §4 · pp. 16–17

4.1 Active Energy Loss and Voltage-Dependent Demand

  • On the IEEE 123-bus feeder, NTR provides the dominant loss reduction, while SDNTR and CEDNTR have similar loss levels that cannot be ranked beyond their MIP optimality gaps.With Kz=0.24, CVR’s main contribution is reducing voltage-dependent demand rather than substantially reducing feeder losses; load-energy changes should not be treated as equivalent to loss changes.Source: §4.1 · pp. 17–18, Table 4 · p. 18

4.2 Computational and Numerical Performance

  • The modified feeder uses three substation-rooted radial regions and solves in approximately 206–1,013 s, with small reported balance and conic-relaxation residuals.Radiality, connectivity, voltage, switching, and open-branch-flow constraints are satisfied in all solved configurations.Source: §4 · pp. 16–17, §4.2 · p. 18

4.3 Loading Stress Assessment

  • CEDNTR remains feasible at the tested 120% loading level, while SDN becomes infeasible at 120% after remaining feasible through 110%.At 120% loading, CEDNTR’s substations reach approximately 83.5%, 99.4%, and 91.3% utilization; SDN’s loading boundary is governed by Substation 3 capacity rather than branch thermal limits.Source: §4.3 · pp. 18–19, Figure 13 · p. 19

5. Conclusion

The paper presents a day-ahead MISOCP framework that jointly coordinates CVR and NTR in active distribution networks. Its results show complementary benefits that vary with operating conditions, including lower losses and demand and improved loading robustness.

5. Conclusion

  • On the IEEE 33-bus system under mixed ZIP loading, NTR reduces active energy loss by approximately 2.50%, while CEDNTR reduces it by 2.91% relative to SDN and active load by 2.46% relative to SDNTR.Under constant impedance loading, CEDNTR achieves approximately 17.65% loss reduction relative to SDN and 14.61% CVR-induced active load reduction relative to SDNTR.Source: §5 · pp. 19–20
  • On the IEEE 123-bus system, NTR reduces active energy losses by approximately 19.3%, while CVR reduces voltage-dependent demand by 2.3 to 2.4%.CEDNTR remains feasible at 120% loading while SDN becomes infeasible.Source: §5 · p. 20
  • The coordinated CEDNTR load-reduction response to DER portfolio scaling is nonmonotonic, with the strongest reduction at the investigated 20% penetration level.The paper concludes that benefits depend on load composition, DER scaling, feeder topology, voltage margins, and source capacity constraints.Source: §5 · p. 20

Related papers

Loading 2610.17122v1…