TY - JOUR
T1 - Distributionally Robust Chance-Constrained Optimal Power Flow with Uncertain Renewables and Uncertain Reserves Provided by Loads
AU - Zhang, Yiling
AU - Shen, Siqian
AU - Mathieu, Johanna L.
N1 - Publisher Copyright:
© 1969-2012 IEEE.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/3
Y1 - 2017/3
N2 - Aggregations of electric loads can provide reserves to power systems, but their available reserve capacities are time-varying and not perfectly known when the system operator computes the optimal generation and reserve schedule. In this paper, we formulate a chance constrained optimal power flow problem to procure minimum cost energy, generator reserves, and load reserves given uncertainty in renewable energy production, load consumption, and load reserve capacities. Assuming that uncertainty distributions are not perfectly known, we solve the problem with distributionally robust optimization, which ensures that chance constraints are satisfied for any distribution in an ambiguity set built upon the first two moments. We use two ambiguity sets to reformulate the model as a semidefinite program and a second-order cone program and run computational experiments on the IEEE 9-bus, 39-bus, and 118-bus systems. We compare the solutions to those given by two benchmark reformulations; the first assumes normally distributed uncertainty and the second uses large numbers of uncertainty samples. We find that the use of load reserves, even when load reserve capacities are uncertain, reduces operational costs. Also, the approach is able to meet reliability requirements, unlike the first benchmark approach and with lower computation times than the second benchmark approach.
AB - Aggregations of electric loads can provide reserves to power systems, but their available reserve capacities are time-varying and not perfectly known when the system operator computes the optimal generation and reserve schedule. In this paper, we formulate a chance constrained optimal power flow problem to procure minimum cost energy, generator reserves, and load reserves given uncertainty in renewable energy production, load consumption, and load reserve capacities. Assuming that uncertainty distributions are not perfectly known, we solve the problem with distributionally robust optimization, which ensures that chance constraints are satisfied for any distribution in an ambiguity set built upon the first two moments. We use two ambiguity sets to reformulate the model as a semidefinite program and a second-order cone program and run computational experiments on the IEEE 9-bus, 39-bus, and 118-bus systems. We compare the solutions to those given by two benchmark reformulations; the first assumes normally distributed uncertainty and the second uses large numbers of uncertainty samples. We find that the use of load reserves, even when load reserve capacities are uncertain, reduces operational costs. Also, the approach is able to meet reliability requirements, unlike the first benchmark approach and with lower computation times than the second benchmark approach.
KW - Chance-constrained optimal power flow (CC-OPF)
KW - convex optimization
KW - load control
KW - moment-based ambiguity set
KW - uncertain reserves
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U2 - 10.1109/TPWRS.2016.2572104
DO - 10.1109/TPWRS.2016.2572104
M3 - Article
AN - SCOPUS:85013840931
VL - 32
SP - 1378
EP - 1388
JO - IEEE Transactions on Power Systems
JF - IEEE Transactions on Power Systems
SN - 0885-8950
IS - 2
M1 - 7478165
ER -