IEEE Power & Energy Magazine - Grid Edge 2023 - 93

In this example, a three-phase, unbalanced, 11,000-node
test feeder was constructed by connecting the IEEE 8,500node
test feeder with a modified Electric Power Research
Institute (EPRI) Circuit 7. In this example, a node is an
electrical node where all voltages are equivalent. Figure 6
depicts the single-line diagram of the feeder, where the line
width is proportional to the nominal power flow on it, so
a thicker blue line has more power flowing through it. The
primary side of the feeder was modeled in detail, whereas
the loads on the secondary side (which is an aggregation of
several loads in this system) are lumped into corresponding
distribution transformers, resulting in a 4,521-node network
with 1,335 aggregated loads. We grouped the nodes into four
large cells (dotted circles) that were physically colocated and
into a collection of other scattered nodes not inside these
cells, as illustrated in Figure 6. Cell 1 contains 357 nodes
with controllable loads, cell 2 contains 222, cell 3 contains
310, and cell 4 contains 154. Cell 4 represents the EPRI test
circuit. We fixed the remaining loads on all 292 nodes not
included in the four large cells.
To evaluate how well voltage regulation was enabled by the
control algorithms, the three-phase, nonlinear power flow model
was simulated using OpenDSS, a power flow solver. Figure 7
illustrates the output of the simulations under different voltage
controls (voltage without control in blue, voltage with a
default local controller in orange, and voltage with the OPF controller
in green). The voltage without control (blue) demonstrates
a large variation in voltage control
between 0.8 and 1.0 p.u. The local
controller (orange) demonstrated several
locations of undervoltage (lower
than 0.95 p.u.). In contrast, the OPF
control (green) was able to maintain
the voltage magnitudes of all the
nodes within the bound from 0.95
to 1.05 p.u. by incorporating global
information. In contrast, the default
control of the regulators and capacitors
could not guarantee that all the voltages
were within this bound. Of note
in Figure 7 are the nodes located on the
right, which present a tight grouping
for comparison. These points represent
the EPRI circuit and did not have
significant voltage changes because
their initial conditions were within the
normal operating parameters.
The simulation results showed
that an improvement of more
than 10-fold in the speed of convergence
can be achieved by the
hierarchical distributed method
compared with the centrally coordinated
implementation, without losing
any optimality. This significant
november/december 2020
improvement in convergence speed makes real-time grid
optimization and control, as well as fast recovery from blackout
conditions, possible for large distribution systems.
These results demonstrate how the hierarchical distributed
implementation of the primal-dual gradient algorithm
to solve an OPF problem achieves the objective to minimize
both the total cost over all the controllable DERs and the
cost associated with the total network load, subject to voltage
regulation constraints. The proposed implementation is
scalable to large distribution feeders comprising networked
devices, and it reduces the computational burden compared
with the centrally coordinated primal-dual algorithm by
using the information structure of the AEGs. To the best
of our knowledge, this simulation demonstrates the largest
optimization-based control of a power system to date, but we
are working on even larger simulations.
Large-Scale Simulations
There is a significant challenge to integrate multiple technologies
into seamless and resilient operating energy systems
with large numbers ()
108
of controllable devices. One of the
biggest obstacles to understanding how these systems will
function at scale is to create and test a computational framework
that enables the design and analysis of optimization and
control approaches for these highly distributed energy systems.
To enable this vision of AEGs of the future, advanced
computational techniques-such as artificial intelligence,
CC
RC 3
RC 2
RC 4
RC 1
Cell 1
Cell 2
Cell 3
Cell 4 (EPRI Circuit 7)
figure 6. The 11,000-node test feeder constructed from the IEEE 8,500-node test
feeder and a modified EPRI Circuit 7 (Cell 4). Four AEG cells were formed for this
experiment. The higher level cell controller (CC) passes information (purple lines) to
the regional cell (RC) controller and to individual nodes that are not located within
a cell. The blue lines illustrate the physical layout of the distribution feeder, and the
thickness of the line indicates the amount of power flowing through the line.
ieee power & energy magazine
93
IEEE Power & Energy Magazine - Grid Edge 2023

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