# US 10,770,901 B2 · Systems and methods for optimally delivering electrical energy in a network

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- Number: US 10,770,901 B2
- Document ID: US10770901B2
- Status: Granted
- Kind: B2
- Application number: 15/946,605
- Filed: 2018-04-05
- Published: 2018-10-11
- Granted: 2020-09-08
- Earliest claimed: 2017-04-07
- Assignees: Nexant, Inc.
- Applicants: Nexant, Inc.
- Inventors: Joseph M. Bright; Mauro Prais
- Web page: https://patentgrep.com/patent/US10770901B2

## CPC

- H02J 3/381: {Dispersed generators}
- H02J 3/46: Controlling the sharing of generated power between the generators, sources or networks
- G05B 13/041: {in which a variable is automatically adjusted to optimise the performance}
- H02J 3/38: Arrangements for feeding a single network from two or more generators or sources in parallel; Arrangements for feeding already energised networks from additional generators or sources in parallel
- H02J 2103/30: Simulating, planning, modelling, reliability check or computer assisted design [CAD] of electric power networks
- Y02E 40/70: Smart grids as climate change mitigation technology in the energy generation sector
- Y02E 60/00: Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y04S 10/50: Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
- Y04S 40/20: Information technology specific aspects, e.g. CAD, simulation, modelling, system security
- H02J: ELECTRIC POWER NETWORKS; CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G)
- Y02E: REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y04S: SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS

## Abstract

A method for delivering an energy resource on a network includes receiving constraints, a first objective function, and a second objective function. The constraints represent electrical load capacities of elements of the network. The constraints and the first objective function are used to identify (i) a load matrix embodying a set of optimal electrical loads for each of the plurality of elements of the power grid and (ii) a corresponding first feature matrix. The load matrix and the first feature matrix optimize the first objective function and satisfy the constraints. If the load matrix and first feature matrix indicate a non-binding fully loaded (NBFL) constraint, the second objective function is used to identify a second feature matrix which optimizes both the first and second objective functions while satisfying the constraints. The second feature matrix assigns a non-zero value to at least one previously identified NBFL constraint.

## Claims

### Claim 1

A method for optimally delivering electrical energy comprising:
receiving a first objective function and a second objective function for optimizing delivery of an energy resource over a power grid;
receiving a set of constraints representing electrical load capacities of a plurality of elements of the power grid;
executing a first optimization process, using the set of constraints and the first objective function, to identify (i) a load matrix embodying a set of optimal electrical loads for each of the plurality of elements of the power grid and (ii) a first feature matrix representing values corresponding to the optimal electrical loads, wherein the load matrix and first feature matrix optimize the first objective function and satisfy the set of constraints;
determining that one or more of the elements of the plurality of elements is fully loaded when the optimal load of the respective one or more elements is equal to the electrical load capacity of the respective one or more elements;
determining that one or more of the elements of the plurality of elements is non-binding when the value corresponding to the respective one or more elements is zero; and
in response to determining that the load matrix includes an element that is both non-binding and fully loaded:
performing a second optimization process, using the first feature matrix and the second objective function as inputs, to identify a second feature matrix which optimizes the second objective function, wherein the second feature matrix preserves the optimality of the first objective function and satisfies the set of constraints, and wherein the second feature matrix assigns a non-zero value to the element that was determined to be non-binding and fully-loaded; and
transmitting the first load matrix and the second feature matrix to the least one power generator to instruct the at least one power generator to generate electrical power.

### Claim 2 (depends on 1)

The method of claim 1, wherein the elements of the power grid include at least one of an electrical conduit and a power generator.

### Claim 3 (depends on 2)

The method of claim 2, wherein the electrical load capacity is a maximum current which the electrical conduit can transmit without exceeding 100° C.

### Claim 4 (depends on 3)

The method of claim 3, wherein the electrical load capacity is determined by at least one of IEEE Standard 738, CIGRE TB 207, and EPRI Dynamp.

### Claim 5 (depends on 1)

The method of claim 1, wherein the second objective function is a function of shadow values of non-binding fully loaded constraints of the power grid.

### Claim 6 (depends on 1)

The method of claim 1, wherein the second objective function is a measure of disparity in values of the energy resources.

### Claim 7 (depends on 6)

The method of claim 6, wherein the second objective function is based on a sum of squares of differences between an average and each value in the second feature matrix.

### Claim 8 (depends on 7)

The method of claim 7, wherein the second objective function is
∑
m
=
1
Periods
⁢
⁢
∑
i
=
1
Buses
⁢
⁢
(
P
i
,
m
⁡
(
α
_
)
-
P
_
l
⁡
(
α
_
)
)
2
where α's are shadow values of non-binding fully loaded (NBFL) constraints, α is a matrix of the α's, Pi,m is a clearing value of an ith bus in a period m, Pl is the average clearing value of the ith bus across all periods.

### Claim 9 (depends on 1)

The method of claim 1, wherein the second objective function is
∑
i
=
1
N
⁢
⁢
TCCs
⁢
⁢
TCC
i
×
CP
i
where N Transmission Congestion Contracts (TCCs) is a number of TCCs, TCCi is energy awarded by the ith TCC, and CPi is a clearing value of the energy awarded to the ith TCC.

### Claim 10 (depends on 1)

The method of claim 1, wherein the second objective function is
∑
i
=
1
N
⁢
⁢
TCC
⁢
⁢
CF
⁢
⁢
TCC
i
×
CP
i
where N TCC CF is a number of counterflow TCCs, TCCi is energy awarded by the ith TCC, and CPi is a clearing value of the energy awarded to the ith TCC.

### Claim 11 (depends on 1)

The method of claim 1, wherein the second objective function is
∑
i
=
1
NGen
⁢
⁢
MW
i
×
LMP
i
where NGen is a number of power generators, MWi is the amount of power supplied from the ith generator, and LMPi is a locational based marginal value of the power from the ith generator.

### Claim 12 (depends on 1)

The method of claim 1, wherein the second objective function is
∑
i
=
1
N
⁢
⁢
Consumers
⁢
⁢
MW
i
×
LMP
i
where NConsumers is a number of consumers, MWi is an amount of power consumed by the ith consumer, and LMPi is a locational based marginal value of power consumed by the ith consumer.

### Claim 13 (depends on 1)

The method of claim 1, wherein the second objective function is
∑
i
=
1
N
⁢
⁢
Virtual
⁢
⁢
MW
i
×
LMP
i
where NVirtual is a number of virtual bidders, MWi is an amount of power bought or sold by the ith virtual bidder, and LMPi is a locational based marginal value of the power bought or sold by the ith virtual bidder.

### Claim 14 (depends on 1)

The method of claim 1, wherein the second objective function is
(
∑
i
=
1
N
⁢
⁢
Consumers
⁢
⁢
MW
i
×
LMP
i
-
∑
j
=
1
NGen
⁢
⁢
MW
j
×
LMP
i
)
where NConsumers is a number of consumers, MWi is an amount of power consumed by the ith consumer, and LMPi is the locational based marginal value of the power consumed by the ith consumer, NGen is the number of power generators, MWj is the amount of power supplied from the jth generator, and LMPj is a locational based marginal value of the power from the jth generator.

### Claim 15 (depends on 1)

The method of claim 1, wherein the second optimization process receives optimality-preserving value ranges from the first optimization process.

### Claim 16 (depends on 1)

The method of claim 1, wherein the second optimization is performed using at least one of linear programming and quadratic programming.

### Claim 17 (depends on 1)

The method of claim 1 wherein the second optimization is performed using interior-point methods.

### Claim 18 (depends on 1)

The method of claim 1, wherein the second optimization is performed using at least one of an ellipsoid algorithm, a Karmarkar's projective algorithm, affine scaling, barrier function algorithm, and a path-following algorithm.

### Claim 19 (depends on 1)

The method of claim 1, wherein the second optimization is performed using at least one of a Lagrangian multiplier, an active set algorithm, an augmented Lagrangian algorithm, a conjugate gradient algorithm, and a gradient projection algorithm.

### Claim 20 (depends on 1)

The method of claim 1, wherein the energy resource is at least one of electrical energy and an electrical energy derivative.

### Claim 21 (depends on 1)

The method of claim 1, wherein optimizing the first objective function includes one of minimizing the second objective function and maximizing the first objective function.

### Claim 22 (depends on 1)

The method of claim 1, wherein optimizing the second objective function includes one of minimizing the second objective function and maximizing the second objective function.

### Claim 23

A system for delivering an energy resource, the system comprising:
a user interface configured to receive:
a first objective function for optimizing distribution of an energy resource,
a set of constraints including a representation of electrical load capacities of a plurality of elements of a power grid, and
a second objective function for assigning value to the energy resource, a processor configured to execute optimization processes; and
non-transitory, computer-readable memory storing instructions which, when executed by the processor, cause the processor to:
identify, using the set of constraints and the first objective function, both:
(i) a load matrix embodying a delivery of the energy resource over the power grid, and
(ii) a first feature matrix representing values corresponding to the load matrix, each of which optimize the first objective function while satisfying the set of constraints;
determine whether the load matrix indicates that at least one element of the plurality of elements is fully loaded;
determine whether the first feature matrix includes a zero-value corresponding to a fully loaded element; and
in response to determining that the first feature matrix includes a zero-value corresponding to a fully loaded element, identify, using the first feature matrix and the second objective function, a second feature matrix which optimizes the second objective function and which represents values corresponding to the load matrix, the second feature matrix preserving the optimization of the first objective function and satisfying the set of constraints, wherein the second feature matrix is not equal to the first feature matrix,
transmit the load matrix and the second feature matrix to at least one power generator to instruct the at least one power generator to generate electrical power.

### Claim 24 (depends on 23)

The system of claim 23, further comprising the power grid.

### Claim 25 (depends on 23)

The system of claim 23, wherein the elements of the power grid include at least one of an electrical conduit and a power generator.

### Claim 26 (depends on 23)

The system of claim 23, wherein the electrical load capacity is a maximum current which the electrical conduit can transmit without exceeding 100° C.

### Claim 27 (depends on 23)

The system of claim 23, wherein the second objective function is a measure of disparity in values of the energy resources.

### Claim 28 (depends on 23)

The system of claim 23, wherein the second objective function is
∑
m
=
1
np
⁢
⁢
∑
i
=
1
n
⁢
⁢
(
P
i
,
m
⁡
(
α
_
)
-
P
_
l
⁡
(
α
_
)
)
2
where n is a number of network elements in the power grid, np is a number of periods, Pi,m is a value of the ith element in the mth period, α is a matrix of shadow values of non-binding fully loaded constraints of the power grid, and Pl is the average value.

### Claim 29 (depends on 23)

The system of claim 23, wherein the second optimization is performed using interior-point methods.

### Claim 30 (depends on 23)

The system of claim 23, wherein the energy resource is at least one of electrical energy and an electrical energy derivative.

### Claim 31

A system for delivering an energy resource, the system comprising:
a processor configured to:
receive a first objective function and a second objective function for optimizing delivery of an energy resource over a power grid;
receive a set of constraints representing electrical load capacities of a plurality of elements of the power grid;
execute a first optimization process, using the set of constraints and the first objective function, to identify (i) a load matrix embodying a set of optimal electrical loads for each of the plurality of elements of the power grid and (ii) a first feature matrix representing values corresponding to the optimal electrical loads, wherein the load matrix and first feature matrix optimize the first objective function and satisfy the set of constraints;
determine that one or more of the elements of the plurality of elements is fully loaded when the optimal load of the respective one or more elements is equal to the electrical load capacity of the respective one or more elements;
determine that one or more of the elements of the plurality of elements is non-binding when the value corresponding to the respective one or more elements is zero; and
in response to determining that the load matrix does not include an element that is both non-binding and fully loaded:
transmit the first load matrix and the first feature matrix to at least one power generator to instruct the at least one power generator to generate electrical power; and
in response to determining that the load matrix includes an element that is both non-binding and fully loaded:
perform a second optimization process, using the first feature matrix and the second objective function as inputs, to identify a second feature matrix which optimizes the second objective function, wherein the second feature matrix preserves the optimality of the first objective function and satisfies the set of constraints, and wherein the second feature matrix assigns a non-zero value to the element that was determined to be non-binding and fully-loaded; and
transmit the first load matrix and the second feature matrix to the least one power generator to instruct the at least one power generator to generate electrical power.