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Distributed control of reactive power flow in a radial distribution circuit with high photovoltaic penetration
Konstantin Turitsyn, Petr Sulc, Scott Backhaus, Michael Chertkov
TL;DR
High PV penetration creates voltage-regulation and loss-minimization challenges that conventional equipment may not address quickly. The paper optimizes reactive-power dispatch from PV inverters in a radial circuit and compares centralized and local control. In the modeled circuit, reactive-power dispatch approaches 20% loss savings, while a simple local scheme achieves about 95% of the maximum possible savings.
Problem
Time-variable, distributed PV complicates voltage regulation and creates two-way power flows that conventional utility-scale equipment may not handle adequately or quickly.
Method
The paper uses a LinDistFlow-based convex optimization to dispatch PV-inverter reactive power for loss minimization under voltage and inverter-capacity constraints, comparing global and local schemes.
Results
Energy savings approach 20% at very high PV penetrations, while the local scheme achieves about 95% of the maximum possible savings for the prototypical circuit and loads.
Takeaways & Limitations
For the prototypical circuit, power dissipation decreases and power quality increases with PV penetration and excess inverter apparent-power capacity, while local control performs nearly as well as global control.
Takeaways & Limitations
The study is preliminary, focuses on a radial prototype, and notes that extending the approach to loopy networks presents an algorithmic challenge.
Abstract
from arXiv · showhide
We show how distributed control of reactive power can serve to regulate voltage and minimize resistive losses in a distribution circuit that includes a significant level of photovoltaic (PV) generation. To demonstrate the technique, we consider a radial distribution circuit with a single branch consisting of sequentially-arranged residential-scale loads that consume both real and reactive power. In parallel, some loads also have PV generation capability. We postulate that the inverters associated with each PV system are also capable of limited reactive power generation or consumption, and we seek to find the optimal dispatch of each inverter's reactive power to both maintain the voltage within an acceptable range and minimize the resistive losses over the entire circuit. We assume the complex impedance of the distribution circuit links and the instantaneous load and PV generation at each load are known. We compare the results of the optimal dispatch with a suboptimal local scheme that does not require any communication. On our model distribution circuit, we illustrate the feasibility of high levels of PV penetration and a significant (20% or higher) reduction in losses.
I. INTRODUCTION
Higher, time-variable PV generation challenges conventional voltage regulation because utility-scale equipment is relatively slow and distributed power flows become harder to estimate. The paper motivates using PV inverters for coordinated, high-speed voltage regulation and loss optimization.
- Motivation: Higher penetrations of time-variable PV generation create new voltage-regulation challenges in distribution systems.Existing regulation equipment is suited to relatively small and slowly changing load and voltage fluctuations.
- Motivation: Distributed residential PV makes power flows harder to estimate from current measurements at only a few circuit locations.PV injects real power at many points, and flows increasingly become two-way.
- Motivation: Conventional ULTCs, SVRs, and SCs may be insufficient for adequate voltage regulation under two-way flows and rapid PV variability.PV variability can occur faster than the operation of these devices.
- Motivation: Present interconnection standards require grid-tied PV inverters to operate at unity power factor without reactive-power control.The paper discusses changing these standards to enable high-speed voltage regulation by inverters.
- Motivation: Reactive-power-enabled inverters require excess apparent-power capacity, whose appropriate size depends on control schemes coordinating responses to voltage and power-flow changes.The paper identifies this sizing question as outstanding.
II. INVERTER AS A LIMITED REGULATOR OF LOCAL REACTIVE POWER FLOW.
The paper models PV inverters as limited, rapidly dispatchable reactive-power regulators and compares centralized coordination with local control. Reactive-power capability shrinks as real PV output approaches inverter apparent-power capacity.
- Inverter capability: PV inverters can supply or consume reactive power when apparent-power capacity exceeds real PV output.The available reactive power is bounded by the inverter capability.
- Inverter capability: Reactive power can be dispatched on a cycle-to-cycle timescale, providing a mechanism for rapid voltage regulation.This speed addresses variability that conventional utility equipment may not handle quickly.
- Inverter capability: Available reactive-power range decreases to zero as PV real-power output approaches inverter apparent-power capacity.The reactive-power bound follows the inverter’s apparent-power constraint.
- Control strategies: The paper compares local dispatch based on local or nearest-neighbor measurements with centralized dispatch using circuit-wide voltage and power-flow information.Centralized algorithms can use enhanced communications and power-flow models to dispatch individual inverters.
- Control strategies: Power-line-carrier communication may be too slow to update voltage and power measurements quickly enough for some schemes.This motivates local schemes that do not depend on high-speed communication.
III. POWER FLOW. OPTIMIZATION OF LOSSES AND VOLTAGE CONTROL.
The paper formulates reactive-power dispatch as a loss-minimization problem subject to voltage and inverter-capacity constraints. A LinDistFlow approximation makes the problem a convex quadratic program with a unique, efficiently computable solution.
- Power-flow model: The radial-network model uses DistFlow equations to represent real-power, reactive-power, and voltage flows along circuit links.Link impedance and node power extraction determine the flow relationships.
- Power-flow model: Node power extraction combines local consumption with PV generation, while inverter-generated reactive power is the adjustable control variable.Real load and PV generation are uncontrolled inputs in this formulation.
- Optimization objective and constraints: The optimization minimizes circuit energy dissipation while enforcing voltage bounds and inverter reactive-power capability constraints.Voltage is constrained approximately within 1 ± 0.05 per unit in squared-voltage form.
- Optimization objective and constraints: The general DistFlow problem is nonconvex and may have multiple solutions, so the paper uses the DC-based LinDistFlow approximation.The approximation reduces computational burden for the model distribution circuit.
- Optimization objective and constraints: The resulting formulation is a convex quadratic problem with linear constraints, a unique solution, and efficient computation.The paper argues that this approximation is well justified for its rural distribution-circuit example.
IV. DESCRIPTION OF THE PROTOTYPICAL RURAL
The study models a sparsely loaded rural radial distribution circuit with residential loads and PV-equipped nodes, varying PV penetration and inverter reactive-power capacity. Its simplified power-flow model is accurate because nonlinear AC terms are much smaller than linear terms under the modeled conditions.
- The prototype is a 7.2 kV rural circuit with constant line impedance of (0.33 + 0.38i)Ω/km.
- The circuit contains 100 load nodes separated by uniformly distributed distances of 200–300 meters.
- Loads consume real power drawn uniformly from 0 to 4 kW and reactive power set relative to their real-power consumption.
- PV-equipped nodes generate 1 kW each, while the penetration fraction r and common inverter apparent-power capacity s are varied.
- The modeled nonlinear AC power-flow terms are about 10^4 times smaller than the linear terms, making LinDistFlow results almost indistinguishable from the exact AC model.
V. SIMULATIONS: RESULTS AND DISCUSSIONS
Simulations evaluate reactive-power dispatch across circuit realizations, inverter capacity, PV penetration, and voltage regulation. Global optimization reduces losses and voltage drop, while a simple local controller achieves nearly the global savings in the prototype.
- Results use many random realizations of the prototype, with qualitative and quantitative findings reported as sufficiently robust for a typical sample.
- Energy savings increase monotonically with inverter apparent-power capacity s, with most savings achieved by s = 1.1.
- The local controller requires no communication and sets injected reactive power from local reactive-power consumption subject to inverter limits.
- The local strategy achieves about 95% of the maximum possible savings for the prototypical circuit and load assumptions.
- With r = 90% and s = 2.0, reactive-power dispatch significantly reduces voltage drop along the circuit; global control suppresses line reactive-power flow more effectively than local control.
VI. CONCLUSIONS AND PATH FORWARD
The study finds that reactive-power dispatch reduces dissipation and improves power quality as PV penetration and inverter excess capacity increase. It also identifies broader circuit models, intermediate control strategies, and loopy networks as future directions.
- Power dissipation is reduced and power quality is increased as PV penetration and excess inverter apparent-power capacity increase.
- For the prototype, loss reduction plateaus at relatively low excess apparent power, while local control performs nearly as well as the global solution.
- Different circuit configurations and load profiles must be studied to determine whether the qualitative and quantitative results generalize across cases.
- Intermediate strategies could trade global optimality for local computation, communication, and coordination while narrowing the gap between fully local and fully global control.
- Extending optimization to loopy, highly meshed circuits is an algorithmic challenge, although LinDistFlow is expected to remain polynomially tractable.