Systems, methods and apparatus for improved operation of electricity markets

1. A method of operating a power system to deliver energy at a market clearing price, the method comprising:

receiving constraints within a scheduling and pricing system;

receiving bids with corresponding generation capacity and offers with corresponding load requirements, within the scheduling and pricing system;

applying the constraints, the bids, the generation capacity, the offers, and the load requirements to a quadratic programming model of a market clearing system within the scheduling and pricing system wherein the quadratic programming model includes a relaxation of all pricing constraints that are epsilon proportional to the market clearing price of the constraints;

determining market clearing prices and corresponding generation and load schedules based on optimizing the quadratic programming model of the market clearing system;

distributing the market clearing prices and the corresponding generation and load schedules to a billing and settlement system;

distributing each generation and load schedule to a generation control and load management system; and

controlling operation of generator resources and managing loads by the generation control and load management system to deliver energy to customers based on the generation and load schedules.

2. The method of claim 1 wherein applying the constraints, the bids, the generation capacity, the offers, and the load requirements to the quadratic programming model of the market clearing system includes applying the constraints, the bids, the generation capacity, the offers, and the load requirements to the quadratic programming model that includes a sum of squares of the market clearing prices multiplied by a fraction of epsilon added into an objective function of the quadratic programming model.

3. The method of claim 2 wherein epsilon is approximately 10 −6 or smaller.

4. The method of claim 3 wherein the fraction of epsilon is ½.

5. The method of claim 1 wherein the quadratic programming model of the market clearing system is expressed as:

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wherein z represents welfare, j represents a first integer index value for market constraint variables from 1 to n; n represents a total number of market constraint variables in a market; c j represents price coefficients of the bids; x j represents levels of supply or demand at price c j and is a non-negative number; ε i represents positive numbers; μ i represents technical variables introduced only for constraints that are being priced and which will turn out to be equal to prices by which the market gets settled; a ij represents a coefficient of market constraint variable j; b i represents constraints; i represents a second integer index value from 1 to m; and m represents a total number of constraints specified for each time interval of the market.

6. A system for delivering energy at a market clearing price, the system comprising:

a scheduling and pricing system including a quadratic programming model of a market clearing system;

a plurality of input information sources in communication with the scheduling and pricing system;

a generation control and load management system in communication with the scheduling and pricing system; and

a billing and settlement system in communication with the scheduling and pricing system,

wherein the scheduling and pricing system is operative to receive constraints, bids with corresponding generation capacity, and offers with corresponding load requirements from the plurality of input information sources,

wherein the scheduling and pricing system is further operative to:

determine market clearing prices and corresponding generation and load schedules based on optimizing the quadratic programming model of the market clearing system with the received constraints, bids with corresponding generation capacity, and offers with corresponding load requirements, wherein the quadratic programming model includes a relaxation of all pricing constraints that are epsilon proportional to the market clearing price of the constraints;

distribute the market clearing prices and the corresponding generation and load schedules to the billing and settlement system; and

distribute each generation and load schedule to the generation control and load management system wherein the generation control and load management system is operative to direct control operation of generator resources and manage loads to deliver energy to customers based on the generation and load schedule.

7. The system of claim 6 wherein the quadratic programming model includes a sum of squares of the market clearing prices multiplied by a fraction of epsilon added into an objective function of the quadratic programming model.

8. The system of claim 7 wherein epsilon is approximately 10 −6 or smaller.

9. The system of claim 8 wherein the fraction of epsilon is ½.

10. The system of claim 6 wherein the quadratic programming model of the market clearing system is expressed as:

min

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{

z

=

∑

j

⁢

c

j

⁢

x

j

+

1

2

⁢

∑

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i

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μ

i

2

|

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j

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a

ij

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x

j

+

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i

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μ

i

=

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=

1

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,

m

⋀

x

j

≥

0

,

j

=

1

,

…

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,

n

}

wherein z represents welfare, j represents a first integer index value for market constraint variables from 1 to n; n represents a total number of market constraint variables in a market; c j represents price coefficients of the bids; x j represents levels of supply or demand at price c j and is a non-negative number; ε i represents positive numbers; μ i represents technical variables introduced only for constraints that are being priced and which will turn out to be equal to prices by which the market gets settled; a ij represents a coefficient of market constraint variable j; b i represents constraints; i represents a second integer index value from 1 to m; and m represents a total number of constraints specified for each time interval of the market.

11. The system of claim 6 wherein the plurality of input information sources includes at least one of a transmission network database, forecasting applications, an energy management system, and an outage management system.

12. The system of claim 11 wherein the plurality of input information sources includes market participants.

13. A system for delivering energy at a market clearing price, the system comprising:

a processor; and

a memory coupled to the processor and storing processor executable instructions to:

receive constraints within a scheduling and pricing system;

receive bids with corresponding generation capacity and offers with corresponding load requirements, within the scheduling and pricing system;

apply the constraints, the bids, the generation capacity, the offers, and the load requirements to a quadratic programming model of a market clearing system within the scheduling and pricing system, wherein the quadratic programming model includes a relaxation of all pricing constraints that are epsilon proportional to the market clearing price of the constraints;

determine market clearing prices and corresponding generation and load schedules based on optimizing the quadratic programming model of the market clearing system;

distribute the market clearing prices and the corresponding generation and load schedules to a billing and settlement system;

distribute each generation and load schedule to a generation control and load management system; and

control generator resources and manage loads to deliver energy to customers based on the generation and load schedule.

14. The system of claim 13 wherein the instructions to apply the constraints, the bids, the generation capacity, the offers, and the load requirements to the quadratic programming model of the market clearing system includes instructions to apply the constraints, the bids, the generation capacity, the offers, and the load requirements to the quadratic programming model that includes a sum of squares of the market clearing prices multiplied by a fraction of epsilon added into an objective function of the quadratic programming model.

15. The system of claim 14 wherein epsilon is approximately 10 −6 or smaller.

16. The system of claim 15 wherein the fraction of epsilon is ½.

17. The system of claim 13 wherein the quadratic programming model of the market clearing system is expressed as:

min

⁢

{

z

=

∑

j

⁢

c

j

⁢

x

j

+

1

2

⁢

∑

i

⁢

ɛ

i

⁢

μ

i

2

|

∑

j

⁢

a

ij

⁢

x

j

+

ɛ

i

⁢

μ

i

=

b

i

,

i

=

1

,

…

⁢

,

m

⋀

x

j

≥

0

,

j

=

1

,

…

⁢

,

n

}

wherein z represents welfare, j represents a first integer index value for market constraint variables from 1 to n; n represents a total number of market constraint variables in a market; c j represents price coefficients of the bids; x j represents levels of supply or demand at price c j and is a non-negative number; ε i represents positive numbers; μ i represents technical variables introduced only for constraints that are being priced and which will turn out to be equal to prices by which the market gets settled; a ij represents a coefficient of market constraint variable j; b i represents constraints; i represents a second integer index value from 1 to m; and m represents a total number of constraints specified for each time interval of the market.