IEEE Power & Energy Magazine - Grid Edge 2023 - 90

✔ 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)
Aggregated
DER
P, Q Set Points
Power
Measurement
Single
DER
P, Q Set Points
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).
Power
Measurement Unit
Controllable DER
Measurement
Voltage and Current
Measurements
figure 3. These measurements are used as a feedback mechanism for DER
control. Real (P) and reactive (Q) power are used to optimize conditions on the
distribution circuit.
90
ieee power & energy magazine
Hierarchical Communications
and Asynchronous Data
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 consistency
among cells, constraints are
added to the optimization problem
to ensure that adjacent cells agree
on the power flows from one cell
to another. This is known as consensus-based
optimization. Overall,
the resultant feedback-based
online optimization methods need
to provably track the solution of
the convex optimization problems
by modeling well-defined objectives
and constraints for each
cell as well as the consistency
constraints for electrical quantities
that pertain to the cell-to-cell
connections. The feedback-based
method also works for nonconvex
problems; however, analytic proof
of convergence for the feedbackbased
method is very tricky and
not well established. These cell
connections can be geographically
Price Signal
FeedbackBased
Updates
november/december
2020
Power
Measurement
IEEE Power & Energy Magazine - Grid Edge 2023

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