Systems and methods for AC optimal power flow modeling for unbalanced distribution systems
View Patent ↗A system and associated method models behavior of an unbalanced distribution system using a current-voltage (IVACOPF) formulation. Untransposed distribution lines, shunt elements of distribution lines, and detailed representation of distribution transformers and DERs are modeled. The system provides detailed modeling of distribution system including mutual impedances, shunt elements, 3-phase to 1-phase lines. The model has multiple applications for distribution system management, planning, and operation.
1 . A system, comprising:
a processor in communication with a memory, the memory including instructions executable by the processor to:
access state data descriptive of a state of an unbalanced distribution network;
identify one or more unknown parameters of a plurality of parameters of the unbalanced distribution network based on the state data; and
evaluate, based on the state data, a value of the one or more unknown parameters of the unbalanced distribution network using an objective function constrained by a set of unbalanced distribution network constraints that collectively model operation of the unbalanced distribution network, the set of unbalanced distribution network constraints incorporating, for a three-phase distribution line of the unbalanced distribution network that is connected to a first bus of a plurality of buses of the unbalanced distribution network:
a mutual current coupling, a mutual voltage coupling, and resultant line power losses within each phase and between each respective phase of the three-phase distribution line; and
a shunt admittance impact within each phase and between each respective phase of the three-phase distribution line.
2 . The system of claim 1 , the set of unbalanced distribution network constraints further incorporating, for the first bus connected to the three-phase distribution line of the unbalanced distribution network, one or more of: an injected active power and an injected reactive power associated with one or more of: a distributed energy resource, a customer load, a distribution transformer, and a capacitor bank of the unbalanced distribution network.
3 . The system of claim 2 , the injected active power incorporating a no-load power loss associated with the distribution transformer.
4 . The system of claim 2 , wherein the distributed energy resource includes a renewable energy resource that injects power into the unbalanced distribution network.
5 . The system of claim 2 , the memory further including instructions executable by the processor to:
iteratively determine the injected active power associated with the bus and the phase, the injected active power being expressed as a convexified linear approximation of injected active power.
6 . The system of claim 2 , the memory further including instructions executable by the processor to:
iteratively determine the injected reactive power associated with the bus and the phase, the injected reactive power being expressed as a convexified linear approximation of injected reactive power.
7 . The system of claim 1 , the memory further including instructions executable by the processor to:
generate, based on the state data and based on the values of the one or more unknown parameters of the unbalanced distribution network, a graphical representation for display at a display device.
8 . The system of claim 7 , the graphical representation showing a system topology of the unbalanced distribution network that includes values of the one or more unknown parameters of the unbalanced distribution network.
9 . The system of claim 1 , the memory further including instructions executable by the processor to:
access optimization data indicative of an optimization goal for optimization of the unbalanced distribution network, the optimization data specifying the one or more unknown parameters of the unbalanced distribution network to be optimized according to one or more optimization rules.
10 . The system of claim 9 , the memory further including instructions executable by the processor to:
apply a control input to one or more components of the unbalanced distribution network based on the values of the one or more unknown parameters of the unbalanced distribution network.
11 . The system of claim 1 , the objective function including a convex quadratically constrained quadratic programming formulation that jointly determines an operation cost and distributed energy resource curtailment for optimal scheduling of distributed energy resources of the unbalanced distribution network.
12 . The system of claim 1 , the objective function including a quadratic programming formulation that minimizes a difference between modeled values and measured values for estimating a state of one or more components of the unbalanced distribution network.
13 . The system of claim 12 , the objective function being subject to a constraint that incorporates reactive power consumption of one or more components of the unbalanced distribution network.
14 . The system of claim 12 , the objective function modeling a potential outage associated with a portion of the unbalanced distribution network as a state of a switch associated with the portion of the unbalanced distribution network, and wherein evaluating the objective function enables estimation of the state of the switch based on the estimated state of one or more components of the unbalanced distribution network with respect to the set of unbalanced distribution network constraints.
15 . The system of claim 1 , the memory further including instructions executable by the processor to:
iteratively simulate operation of the unbalanced distribution network based on the objective function and the set of unbalanced distribution network constraints resulting in simulation data indicative of a simulated state of the unbalanced distribution network;
measure a state of one or more components of the unbalanced distribution network based on measurements accessed by the processor from one or more components of the unbalanced distribution network; and
adjust one or more parameters of the unbalanced distribution network, the objective function and/or the set of unbalanced distribution network constraints based on a difference between the simulated state of the unbalanced distribution network and the state of the unbalanced distribution network as measured.
16 . The system of claim 1 , the objective function including a formulation that determines an error of the unbalanced distribution network based on an estimated state of one or more components of the unbalanced distribution network with respect to the set of unbalanced distribution network constraints.
17 . The system of claim 1 , the objective function including a formulation that optimizes a resource mix of the unbalanced distribution network with respect to one or more resource limitations based on an estimated state of one or more components of the unbalanced distribution network with respect to the set of unbalanced distribution network constraints.
18 . The system of claim 1 , the set of unbalanced distribution network constraints incorporating:
a droop control constraint for a photovoltaic inverter of the unbalanced distribution network that adaptively adjusts generation or absorption of reactive power by the photovoltaic inverter based on a value of a local voltage with respect to one or more local voltage operating zones, the one or more local voltage operating zones being adaptively adjusted based on the state data of the unbalanced distribution network.
19 . A method, comprising:
accessing state data descriptive of a state of an unbalanced distribution network;
identifying one or more unknown parameters of a plurality of parameters of the unbalanced distribution network based on the state data; and
evaluating, based on the state data, a value of the one or more unknown parameters of the unbalanced distribution network using an objective function constrained by a set of unbalanced distribution network constraints that collectively model operation of the unbalanced distribution network, the set of unbalanced distribution network constraints incorporating, for a three-phase distribution line of the unbalanced distribution network that is connected to a first bus of a plurality of buses of the unbalanced distribution network:
a mutual current coupling, a mutual voltage coupling, and resultant line power losses within each phase and between each respective phase of the three-phase distribution line; and
a shunt admittance impact within each phase and between each respective phase of the three-phase distribution line.
20 . The method of claim 19 , the set of unbalanced distribution network constraints further incorporating, for the first bus connected to the three-phase distribution line of the unbalanced distribution network, one or more of: an injected active power and an injected reactive power associated with one or more of: a distributed energy resource, a customer load, a distribution transformer, and a capacitor bank of the unbalanced distribution network, the injected active power incorporating a no-load power loss associated with the distribution transformer.