# Phasor-Based Control for Scalable Integration of Variable Energy Resources

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## Abstract

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## 1. Introduction

## 2. The PBC Paradigm: Motivating Examples

#### 2.1. Radial Distribution Feeder

#### 2.1.1. Toy Example 1

#### 2.1.2. Radial Distribution Feeder Simulation

#### 2.2. Parallel Transmission Lines

#### 2.2.1. Toy Example 2

#### 2.2.2. Simulation: Transmission P-V curves

## 3. The PBC Paradigm: Control System Architecture

#### 3.1. Local PBC

#### 3.2. Supervisory PBC

## 4. Scalable Integration of Variable Energy Resources

#### 4.1. Managing Variability

#### 4.2. Layered Architecture

#### 4.3. Strategic Advantages of PBC

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Simple phasor-based control (PBC) example on a typical radial distribution circuit. Two phasor measurement units ($\mu $PMUs) record the voltage phasors ${V}_{0}\angle {\delta}_{0}$ and ${V}_{1}\angle {\delta}_{1}$ at their respective nodes. Arrows depict real and reactive power flows P and Q, which may be in either direction. Resource 1 represents a controllable power source or sink, such as solar PV, battery, or controllable load, that modulates real and reactive power flows ${P}_{1}$ and ${Q}_{1}$.

**Figure 2.**Institute of Electrical and Electronics Engineers (IEEE) 13-node Test feeder [29] for PBC simulation with multiple actuators. PMUs at nodes 650 and 632 measure the respective voltage phasors. The local (L)-PBC controller coordinates actuators at nodes 645, 634, and 675 by modulating their power to track a target phasor reference at Node 632 relative to node 650.

**Figure 3.**The target phasor at node 634a and the corresponding L-PBC voltage magnitude response (

**left**) and phase angle response (

**right**) to three disturbances. Different algorithms can be used for tuning proportional-integral (PI) controller gains.

**Figure 4.**Simple contingency example for a meshed transmission network, where a PMU at each of the two nodes measures the respective voltage phasor. Two transmission lines share a path to deliver the combined power ${P}_{12}$, ${Q}_{12}$ from node 1 to node 2. The impedance of each individual line is $r+jx$. A credible contingency event to be addressed by PBC is the loss of one transmission line.

**Figure 5.**Power-Voltage stability curves for a contingency event (magnified for clarity in the right side figure). Operating point A is pre-contingency; points B and C are post-contingency. Without actuation, the loss of a parallel transmission line shifts the curve and forces the system from A to B. By explicitly addressing nodal voltage, PBC drives the system toward operating point C. This avoids dangerous proximity to the nose of the curve, allowing for an improved stability margin without requiring calculation of the new curve.

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## Share and Cite

**MDPI and ACS Style**

von Meier, A.; Ratnam, E.L.; Brady, K.; Moffat, K.; Swartz, J.
Phasor-Based Control for Scalable Integration of Variable Energy Resources. *Energies* **2020**, *13*, 190.
https://doi.org/10.3390/en13010190

**AMA Style**

von Meier A, Ratnam EL, Brady K, Moffat K, Swartz J.
Phasor-Based Control for Scalable Integration of Variable Energy Resources. *Energies*. 2020; 13(1):190.
https://doi.org/10.3390/en13010190

**Chicago/Turabian Style**

von Meier, Alexandra, Elizabeth L. Ratnam, Kyle Brady, Keith Moffat, and Jaimie Swartz.
2020. "Phasor-Based Control for Scalable Integration of Variable Energy Resources" *Energies* 13, no. 1: 190.
https://doi.org/10.3390/en13010190