Local Control of Reactive Power by Distributed Photovoltaic Generators

Konstantin S. Turitsyn; Petr Sulc; Scott Backhaus; Misha Chertkov

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Local Control of Reactive Power by Distributed Photovoltaic Generators

Konstantin S. Turitsyn, Petr Sulc, Scott Backhaus, Misha Chertkov

arXiv:1006.0160v1Jun 1, 2010math.OC

TL;DR

High distributed-PV penetration can degrade voltage quality because rapid generation changes outpace existing regulation equipment. The paper proposes locally dispatching inverter reactive power from instantaneous local measurements, with one circuit-level parameter balancing voltage quality and thermal losses. Simulations show significant improvements across loading and generation regimes, including cases with excess generation.

Problem
High distributed-PV penetration can cause voltage-regulation problems when cloud-driven generation changes are faster than existing utility equipment responds.
Method
The paper uses a local reactive-power control scheme based on local consumption and PV-generation measurements, with parameter K balancing power quality and thermal-loss objectives.
Results
The scheme achieves significant simultaneous improvements in circuit power quality and losses across sunny, overcast, high-load, and low-load regimes.
Takeaways & Limitations
10% of excess inverter capacity s is enough to allow significant reductions in both losses and voltage deviations.

Abstract

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High penetration levels of distributed photovoltaic (PV) generation on an electrical distribution circuit may severely degrade power quality due to voltage sags and swells caused by rapidly varying PV generation during cloud transients coupled with the slow response of existing utility compensation and regulation equipment. Although not permitted under current standards for interconnection of distributed generation, fast-reacting, VAR-capable PV inverters may provide the necessary reactive power injection or consumption to maintain voltage regulation under difficult transient conditions. As side benefit, the control of reactive power injection at each PV inverter provides an opportunity and a new tool for distribution utilities to optimize the performance of distribution circuits, e.g. by minimizing thermal losses. We suggest a local control scheme that dispatches reactive power from each PV inverter based on local instantaneous measurements of the real and reactive components of the consumed power and the real power generated by the PVs. Using one adjustable parameter per circuit, we balance the requirements on power quality and desire to minimize thermal losses. Numerical analysis of two exemplary systems, with comparable total PV generation albeit a different spatial distribution, show how to adjust the optimization parameter depending on the goal. Overall, this local scheme shows excellent performance; it's capable of guaranteeing acceptable power quality and achieving significant saving in thermal losses in various situations even when the renewable generation in excess of the circuit own load, i.e. feeding power back to the higher-level system.

I. INTRODUCTION

High penetration of distributed PV can impair voltage regulation because cloud-driven generation changes outpace existing utility equipment. The paper studies local reactive-power control as a scalable way to address voltage and loss objectives across diverse distribution circuits.

Motivation: High PV penetration can significantly affect distribution-circuit power quality when cloud transients cause rapid generation changes.Existing utility compensation and regulation equipment may respond too slowly to these variations.
Motivation: Reactive-power control by individual PV generators is proposed as an alternative mitigation approach, although current interconnection standards prohibit it.The approach would use excess inverter capacity to generate or consume reactive power for voltage regulation.
Approach: The analysis samples circuit realizations statistically while varying macroscopic loading, spacing, and PV-generation parameters.This includes scenarios with net power export and rising local voltage.
Relation to prior work: The work extends earlier local reactive-power control by examining both circuit losses and power quality rather than loss reduction alone.Earlier work reported almost 80% loss savings relative to centralized full optimization on realistic feeder lines.
Relation to prior work: Prior optimization methods focused mainly on placement or control of a few large reactive-power sources, whereas this problem involves many small sources.The manuscript therefore develops a method suited to distributed PV inverters.

II. INVERTER AS A LIMITED REGULATOR OF LOCAL REACTIVE POWER FLOW.

PV inverters can rapidly provide reactive power when their apparent-power capability exceeds instantaneous PV output, but that capability shrinks as real generation approaches the inverter limit. The paper models this weather- and time-dependent constraint explicitly.

Interconnection constraints: PV inverters must operate at unity power factor under the current distributed-generation interconnection standard.The paper notes that regulations are expected to change to allow reactive-power injection.
Reactive-power capability: When inverter capability s exceeds generated real power p(g), allowable reactive power satisfies |q(g)| ≤ sqrt(s^2 − (p(g))^2).The inverter can supply or consume reactive power on a cycle-to-cycle timescale.
Reactive-power capability: As instantaneous PV output approaches its maximum, the available reactive-power range reaches its minimum.On a clear day with aligned sun angle, p(g) = p(g)_max and reactive capability is smallest.
Reactive-power capability: Reactive-power capability varies across the year, day, and weather because cloud events and imperfect sun alignment reduce p(g) below p(g)_max.Simulations vary p(g) while keeping absolute inverter capability s fixed.

III. OPTIMIZATION OF LOSSES AND VOLTAGE CONTROL

The paper formulates local inverter control as a heuristic multi-objective problem balancing thermal-loss reduction against voltage-deviation control. A single parameter K interpolates between these objectives using local power measurements and inverter constraints.

Circuit model: The radial-circuit model represents real and reactive flows, node extraction, link impedance, and PV inverter reactive-power control.Reactive generation is adjustable only at nodes with PV generation and is bounded by inverter capability.
Circuit model: The LinDistFlow approximation is used when quadratic power-flow terms and voltage deviations are relatively small.The circuit loss rate is then analyzed alongside voltage variation.
Optimization objectives: The control seeks to minimize thermal losses while keeping maximum per-unit voltage deviation within strict regulation bounds.Normal operation uses ϵ ≈ 0.05 for the voltage-deviation bound.
Local control: The local scheme uses q(g)_k based only on local information rather than voltage, to avoid repeatedly burdening PV inverters at lower-voltage locations.The authors describe the resulting scheme as more equitable along the circuit and homogeneous over the line.
Control design: The voltage-oriented control compensates local-load and adjacent-link reactive consumption, while the loss-oriented scheme targets reduced reactive flow.These complementary objectives motivate the combined nonlinear control function.
Control design: K is a single trade-off parameter: K = 1 recovers the loss-oriented scheme, whereas K = 0 recovers the voltage-oriented scheme.This parameter provides the circuit-level adjustment between the two objectives.

IV. DESCRIPTION OF THE PROTOTYPICAL RURAL DISTRIBUTION CIRCUIT

The study models a 250-node sparsely loaded rural distribution circuit with randomized line, load, and PV characteristics. Simulations solve LinDistFlow equations for sampled circuit realizations while varying PV penetration, generation, and operating conditions.

Circuit model: The model is a 250-node sparsely loaded rural circuit with 7.2kV nominal phase-to-neutral voltage and line impedance of (0.33 + 0.38i)Ω/km.Neighboring-node distances are uniformly distributed between 0.2 and 0.3 kilometers.
Circuit model: Load real powers are uniformly distributed from 0 to either 1kW or 2.5kW, while reactive powers are sampled from a distribution tied to real consumption.
PV configuration: PV is installed randomly at either 20% or 50% of nodes, with each PV-enabled node generating uniformly 1kW or 2kW.The inverter capacity is set to s = 2.2kW at PV-enabled nodes.
Simulation procedure: For each case, randomized loads and generation are evaluated by solving the LinDistFlow equations to obtain voltage levels and total losses.The study uses one realization because large-node self-averaging makes results similar across samples.

V. SIMULATIONS: RESULTS AND DISCUSSIONS

Four operating regimes combine two PV penetration levels with sunny and overcast load conditions, including a case with power overgeneration. Varying one common control parameter K reveals improvements in voltage deviation and losses, with different trade-offs across cases.

Operating regimes: Four regimes combine two PV penetration levels with sunny, high-load and overcast, low-load conditions; case 4 has power overgeneration and reversed real-power flow.Cases 1 and 3 have low generation relative to total load but high inverter capacity, while cases 2 and 4 approach or exceed total consumption.
Control evaluation: The controller uses one common K across generating nodes, scans −5 < K < 10, and evaluates total losses L and maximum voltage deviation δV against q^(g)_k = 0.
Voltage quality: Voltage control performs best in cases 2 and 4, while cases 1 and 3 still achieve approximately 0.01 reductions in voltage deviation.Case 4 benefits from compensating reversed real-power flow through increased reactive-power consumption.
Thermal losses: Relative loss minima are 0.93, 0.67, 0.86, and 0.94 for cases 1 through 4, respectively.The largest savings occur in cases 2 and 3; case 4 requires fine tuning of K because reverse-flow losses remain significant.
Multi-objective trade-offs: Cases 1 and 3 have a single joint optimum for losses and voltage deviation, whereas cases 2 and 4 offer a range of K values forming a Pareto set.Case 4 provides the greatest flexibility for trading loss savings against voltage quality.

VI. CONCLUSIONS AND PATH FORWARD

The study proposes a simple local reactive-power control scheme with one circuit-wide parameter balancing power quality and loss reduction. Experiments show simultaneous improvements across tested operating regimes, while identifying sensitivity to tuning and directions for further study.

The scheme adjusts reactive power at distributed PV inverters using local consumption and generation measurements, with one global parameter balancing power flow and power quality.The control is designed as a simple local scheme for circuit-distributed PV inverters.
The local scheme achieves very significant simultaneous improvement in global power quality and reduction of circuit-wide losses across sunny, overcast, large-load, and small-load regimes.The reported performance is described as probably sufficiently close to globally optimal.
10% of excess inverter capacity is enough to allow significant reductions in both losses and voltage deviations.
Over-generation and reversed power flow make the multi-objective optimization more sensitive to parameter changes, requiring more accurate tuning.
Further work includes testing statistical performance variations, studying improved local schemes, incorporating local voltage information, and exploring time-varying or spatially varying control.The proposed extensions include a broadcast-varying parameter and geographically varying coefficients for special situations.