IEEE Power & Energy Magazine - November/December 2020 - 41

colocated or based on aggregators, such as smart-home
aggregators. In this sense, it is worth emphasizing that the
design of the distributed algorithm as well as the overall
communications strategy will depend on the types of actors
participating in the real-time optimization process (e.g., end
customers, cell controllers, or aggregators).
In addition to the influx of DERs, the installation of new
sensing and measurement technologies (e.g., smart meters
and distribution-level phasor measurement units) will drastically improve the observability of grid conditions at the
distribution level. To take advantage of all the available
measurements, algorithms must be able to operate in an
asynchronous way to account for different communications
latencies and for devices that can be controlled at different
timescales (e.g., inverter-interfaced devices are controlled at
fast timescales, whereas thermostatically controlled loads
are controlled every few minutes). Analytic proof of convergence can be tedious, but it is widely accepted that gradientbased algorithms can be implemented asynchronously.

Robustness
In the context of AEGs, robustness includes both reliability and resilience. Reliability is the property to be tolerant
to faults, and resilience is the ability to come back from a
failure to an operational state. For reliable operation, stability analysis can be used at multiple timescales. Resilience to
communications drops and asynchronous operation should
be analytically established through pertinent input-to-state
stability and tracking results. In other words, the AEGs
should be able to continue operating even in the presence
of these faults/errors. Mathematically, iterative optimization

algorithms have been developed to operate with errors in
their estimated parameters, such as gradients. In fact, it can
be shown that a packet loss leads to the computation of primal or dual gradient steps with outdated information. Thus,
cells that can switch from an islanded mode to a larger gridconnected mode may continue operating amid faults and/or
threats to the grid. These properties can be modeled as timevarying constraints in the underlying optimization problem.
Similarly, flexible operation, in which a cell (or a portion of
a cell) switches to an autonomous control setting during a
prolonged communications outage, should be enabled.

Scalability
Figure 5 illustrates an architecture in which communications
among cells occur when performing distributed and/or hierarchical control. As mentioned previously, distributed and
hierarchical control algorithms are scalable and allow for
the control of millions of devices in real time. When using
distributed/hierarchical controls, the problem is broken up
into smaller "cells," and the interactions among cells can be
reconciled using consensus to ensure consistency constraints
for electrical quantities that pertain to the cell-to-cell connections. For example, adjacent cells must agree on the real
and reactive power exchanges at the points of interconnection or overlap.
Real and reactive power set points from the optimization are sent between levels in the hierarchy. Intracellular
communications (on the same level) can be used to ensure
that the set points of the DERs are computed to maximize
the given operational objectives while ensuring that electrical limits are satisfied within the cell. Communications also

Real-Time Algorithm
Real (P) and Reactive (Q ) Set Points

- Actual Value of P and Q at Specific
DER Location Subject to Voltage and
Current Constraints of Location
- Blue Line (DER Output) Tracks
Optimal Solution (Red)

Measurements
of Voltage,
Current, and
Power
Pfin

Power System
(a)

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0 20 40 60 80 100 120 140 160 180
Time
(b)

figure 4. The real-time algorithm tracks the optimal solution. (a) Green dots on the map indicate DER and measurement
locations. (b) The graph shows only the real power (P) set point in red and the actual DER power output in blue for one
DER location.
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IEEE Power & Energy Magazine - November/December 2020

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