IEEE Power & Energy Magazine - November/December 2020 - 40

✔✔ Pervasive metering. Solving optimization problems

using relaxations/linearizations of the ac optimal
power flow (OPF) requires pervasive metering to collect measurements of the noncontrollable loads at all
locations in real time, which might be impractical. One
way to address this problem in the large-scale grid of
the future is to develop and implement distributed state
estimation algorithms that can provide insight into the
state of the system without having to explicitly measure every point of interest.
To address these challenges within the AEG cells, a real-time
optimization framework has been developed at the National
Renewable Energy Laboratory (NREL) under the Network
Optimized Distributed Energy Systems (NODES) program within the U.S. Department of Energy's Advanced
Research Project Agency-Energy (ARPA-E). The framework
can model well-defined objectives and constraints of DERs
located within each cell as well as consistency constraints for
electrical quantities that pertain to the cell-to-cell connections.
By using measurements in the system as a feedback mechanism
and tracking optimal solution trajectories, the resultant feedback-based online optimization methods can cope with inaccuracies in the representation of the ac power flow and avoid
having to measure all the noncontrollable resources. Figure 3
demonstrates how voltage and current measurements are used
as feedback to better track the optimal trajectory of a large-scale
system by sending a price signal that embeds cost functions,
reliability functions, and system constraints.
The algorithm enables DERs to track given performance
objectives while adjusting their power [the real power (P)

and reactive power (Q) set points] to respond to services
requested by grid operators and maintain electrical quantities
within engineering limits. The design of the algorithm leverages primal-dual gradient methods that improve the convergence rate of the optimization problem, allowing the algorithms to take advantage of the structure of the problem and
be solved in real time. The gradient governs which direction
and how fast to search for the next iteration in the optimization, and it can be suitably modified to accommodate appropriate measurements from the distribution network and the
DERs. Primal-dual gradient methods can be implemented in
real time because every gradient iteration is computationally
cheap (very fast to compute); however, this method usually
has a fast convergence rate when referred to the number of
iterations required for the algorithm to converge. The resulting algorithm can cope with inaccuracies in the distribution
system modeling; moreover, it avoids pervasive metering to
gather the state of noncontrollable resources, and it naturally
lends itself to a distributed implementation. Analytic stability and the convergence of optimally tracking the solutions of
the formulated time-varying optimization problem is established. Figure 4 depicts how the real-time algorithm uses
active and reactive power set points for a single DER (blue
line) to track an optimal trajectory (red line).

Hierarchical Communications
and Asynchronous Data

Power
Measurement

To enable the real-time optimization of AEGs with millions of controllable devices, a hierarchical communications
architecture that includes cell-to-cell and cell-to-customer
message passing can be formulated to manage these devices.
Mathematically, to obtain consisAggregated
tency among cells, constraints are
DER
added to the optimization problem
Power
P, Q Set Points
Measurement
to ensure that adjacent cells agree
Price Signal
on the power flows from one cell
Single
to another. This is known as conDER
sensus-based optimization. OverP, Q Set Points
all, the resultant feedback-based
online optimization methods need
to provably track the solution of
the convex optimization problems
Feedbackby modeling well-defined objecBased
Updates
tives and constraints for each
Power
cell as well as the consistency
Measurement
constraints for electrical quantiMeasurement Unit
Controllable DER
ties that pertain to the cell-to-cell
connections. The feedback-based
Voltage and Current
method also works for nonconvex
Measurements
problems; however, analytic proof
of convergence for the feedbackbased method is very tricky and
figure 3. These measurements are used as a feedback mechanism for DER
not well established. These cell
control. Real (P) and reactive (Q) power are used to optimize conditions on the
connections can be geographically
distribution circuit.
40	

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IEEE Power & Energy Magazine - November/December 2020

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