IEEE Power & Energy Magazine - November/December 2020 - 43

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

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IEEE Power & Energy Magazine - November/December 2020

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