Na (Lina) Li Electrical Engineering & Applied Mathematics - - PowerPoint PPT Presentation

Electricity Market for Distribution Networks

Na (Lina) Li

Electrical Engineering & Applied Mathematics Harvard University

University of Maryland, College Park

• Oct. 17th, 2016

Power plant Transmission Users

Supply = Demand

Unresponsive Predictable

Distribution

Time Energy

12 AM 12 AM

Electricity Grid 1.0

Power plant

Controllable Unresponsive Predictable

Users Transmission Distribution

Supply = Demand

Electricity Grid 1.0

Power plant

Forward Energy Market

e.g., Day‐ahead market (one day forward);

Real‐time Energy Market

e.g., Every five minutes in PJM;

Ancillary service market

e.g., Spinning reserve market; (short‐term, unexpected changes)

Controllable Unresponsive Predictable

Users Transmission Distribution

Supply = Demand

Transmission market

• Trans. Market

A Monthly Bill

Power plant

Forward Energy Market

e.g., Day‐ahead market (one day forward);

Real‐time Energy Market

e.g., Every five minutes in PJM;

Ancillary service market

e.g., Spinning reserve market; (short‐term, unexpected changes)

Controllable Unresponsive Predictable

Users Transmission Distribution

Supply = Demand

Transmission market

Market

Renew able energy

www.dsireusa.org/ March2015

2000 4000 6000 1 2 3 4

Seconds since start of day

Real power output (MW)

Source: Rosa Yang, EPRI

Random and intermittent

Denmark’s progress over the past decades

More distributed

• Small CHP (Combined Heat & Power)
• Large CHP (Combined Heat & Power)
• Wind

Power plant

Tomorrow’s Grid 2.0

Transmission Distribution Users

Supply = Demand

Less controllable Highly uncertain Distributed Large scale Responsive Unresponsive

Power plant

Tomorrow’s Grid 2.0

Transmission Distribution Users

Supply = Demand

Smart appliances Storage Electric vehicles

Storage DR appliances EV

Distributed Energy Resources

Solar PVs Wind turbines

Responsive Less controllable Highly uncertain Distributed Large scale

Transforming Electricity Grid: DER

Debate over solar rates simmers in the Nevada desert

February 27, 2016

Sources: PBS

Human Incentive:

Strategic behavior, self-interested, market power

Power Engineering:

Power flow, system dynamics, operation constraints

Uncertainties:

Renewable energy, user’s behavior, emergency

Electricity Market for Distribution Netw orks: Challenges

Human Incentive:

Strategic behavior, self-interested, market power

Power Engineering:

Power flow, system dynamics, operation constraints

Uncertainties:

Renewable energy, user’s behavior, emergency

Electricity Market for Distribution Netw orks: Challenges

Transmit and Distribute Pow er

Kirchhoff’s law

Capacity constraint on any line or node limit the entire flow

Transmit and Distribute Pow er: Kirchhoff’s Law

1 2 3

Line 1‐2 capacity: 25

1 2 3

150 50

Transaction 23 alleviates congestions on line 1‐2

1 2 3

150 100 25

Challenges: An Example

1, 2: generation nodes/buses; 3: load bus (two users) 100 150

How much to pay for public distribution service?

Social Welfare

Benefit Cost Physical Constraints

How much to pay for public distribution service?

Individual How to set the price? Social Welfare

price

(d, g)

How to choose the prices?

Given an convex problem, duality of the optimization provide efficient prices, p*

Social Welfare

Challenges: Nonconvexity

 

,

ij ij ij jk j i j j k

S z S s

 

  

 



c g j j

s s 

 

2 , , (0, ) ,

min + | |

• ver : ( , , , , )
• s. t.

j i i i j i j j i i j

C P U p r I x S v p q        

  



 

2 2 *

, 2 Re ,

ij ij i j i ij ij ij ij

S v v v z S z      

,

i i i

v v v   ,

i i i

p p p   ,

i i i

q q q  

Nonconvex

:

j j j

s p iq   :

j j j

S P iQ  

2 ,

: | |

ij i j

I  

2

: | |

i i

v V 

Nonconvex Optimal Power Flow

Baran & Wu 1989, Chiang & Baran 1990

Convexification gives exact solutions

[Lavaei 2011, Li 2012, Gan 2012, 2013]

Branch flow model

Efficient Prices: Market Equilibrium (d*, g*, p*)

Individual (d*, g*) Social Welfare

Utility Company

p1

*

p2

*

p3

*

User i optimizes

Utility Company

1

p

n

p

n

g

1

d

Utility company gathers requests

MOPF: No info about individuals’ costs and benefits function

Individual i receives the price

Theorem [Li et al. 2012, 2014]: The distributed algorithm converges to market equilibrium over a radial distribution network.

Utility company updates price Individual i updates its request

max ( )

i

d i i i i

B d p d 

Privacy for individuals

A Distributed Algorithm to Reach the Equilibrium

max

• (

)

i

g i i i i

p g C g

Recent work: Distributed algorithms with limited communication.

[2015, 2016]

45

Schematic Diagram of a South California Edison distribution System

Case studies

Substation

• 2
• 1

1 2 bus 3 bus 6 bus 14 bus 54

• 0.01

0.01 0.03 0.05 bus 3 bus 6 bus 14 bus 5

Zoom in

10 20 30 40 50 60 0.03 0.04 0.05 0.06 bus 3 bus 6 bus 14 bus 54 Iterations 10 20 30 40 50 60

Real power calculated by the utility company (MW)

Iteration

Real power calculated by the user (MW)

How about decentralized market?

Bilateral Transaction?

Decentralized?

Delivery Service (in distribution networks)

• Voltage support (constraint):
• Power loss

i i i

v v v  

Challenge: Externality: Any local change induces a (complicated) global change!

Market rule

• Buy voltage right (constraint) at each bus
• Pays for line loss rent of each line

Q: Budget balance on the voltage right and also the power loss? Voltage right at each bus = Σi voltage right bought by transaction i Power losses at each line = Σi Losses paid by transaction i Each Bilateral Transaction

[ , ]

i i i

v v v  [ , ]

j j j

v v v  [ , ]

k k k

v v v 

Bus i Bus j Bus k

Buy voltage right at each bus Pay for line loss rent Line loss Line loss

• Each user/generator maximizes net benefit/profit given elec. prices

Market Prices and Equilibrium

Bus i Bus j Bus k

[ , ]

i i i

v v v  [ , ]

j j j

v v v  [ , ]

k k k

v v v 

Electricity price Electricity price Electricity price Buy voltage right at each bus Pay for line loss rent Line loss Line loss Voltage right price Voltage right price rent rent

• Each user/generator maximizes net benefit/profit given elec. price
• For each unit transaction between any two node i and k
• Elec. Price i = Elec Price j + Sum(Voltage right price*Quantity1)

+ Sum (Line loss rent * Quantity2)

• Voltage right price is 0 if there is excess voltage capacity supply

Market Prices and Equilibrium

Bus i Bus j Bus k

[ , ]

i i i

v v v  [ , ]

j j j

v v v  [ , ]

k k k

v v v 

Electricity price Electricity price Electricity price Buy voltage right at each bus Pay for line loss rent

Question: How to determine Quantity1 ,Quantity2 ?

Line loss Line loss Voltage right price Voltage right price rent rent

How to determine the quantities?

For each unit transaction between any two node i and k Price i = Price j + Sum(Voltage right price*Quantity1) + Sum (Line loss rent * Quantity2)

Quantity1 Quantity2 Prices Duality of the Social Welfare Maximization Budget Balance Constraints

• n Voltage Right and Line Losses

How to determine the quantities?

For each unit transaction between any two node i and k Price i = Price j + Sum(Voltage right price*Quantity1) + Sum (Line loss rent * Quantity2)

Quantity1: Quantity2:

R: resistance V: voltage p: power injection P,Q: real/reactive power flow L: line losses

One Allocation Rule for Voltage Right and Line Losses

Theorem (Li 2015): Under the designed market rule, there exists a competitive market equilibrium that is socially optimal.

User i User j User k

Competitive Market Equilibrium

[ , ]

i i i

v v v  [ , ]

j j j

v v v  [ , ]

k k k

v v v 

Voltage right price Electricity price Voltage right price Electricity price Voltage right price Buy voltage rights at each bus Pay for line loss rent

So far...

Utility Company

Bilateral Transaction? Decentralized?

Scheme 1: Scheme 2:

Markets are efficient

Human Incentive:

Strategic behavior, self-interested, market power

Power Engineering:

Power flow, system dynamics, operation constraints Markets efficiently allocate delivery costs to individuals (transactions)

Uncertainties:

Renewable energy, user’s behavior, emergency

Electricity Market for Distribution Netw orks:

Human Incentive:

Strategic behavior, self-interested, market power

Power Engineering:

Power flow, system dynamics, operation constraints Markets efficiently allocate delivery costs to individuals (transactions)

Uncertainties:

Renewable energy, user’s behavior, emergency

Electricity Market for Distribution Netw orks:

Recall…

Social Welfare

Utility Company

Individuals need to report info.

What if they DON’T report true info.?

Supply Function Bidding for Demand Response

• Supply deficit (or surplus) on electricity:

weather change, unexpected events, …

• Supply is inelastic

Problem: How to allocate the deficit among customers?

load (demand) as a resource to allocate

d

Supply function bidding

• Customer i load to shed:
• Customer i reports a supply function (SF):
• p : price for load shedding
• bi: price sensitivity
• Market‐clearing pricing p:

i

q

p b p b q

i i i

 ) , (

d p b q

i i i





) , (

customer 1: p

1

b

1 1

q b p  customer n:

n n

q b p  p

n

b utility company: deficit d

( ) /

i i

p p b d b 





Load Shedding Cost

• Customer i cost (or disutility) function:
• Social welfare: Optimal Global Cost

) (

i i q

C p

customer i:

p

utility company: deficit d

( )

i i

C q

n

b

1

b min ( ) . .

i

i i q i i i

C q s t q d 

 

Question: Can the supply function bidding achieves the optimal global cost?

Strategic demand response

• Customer i’s net revenue: ui= p qi -Ci (qi)
• Note: Price p is a function of bidding b
• Price‐anticipating, strategic customer

with

• Definition: A supply function profile is a

Nash equilibrium if, for all customers i,

p

n

b p

1

b ))) ( , ( ( )) ( , ( ) ( ) , ( b p b q C b p b q b p b b u

i i i i i i i i

 



) , ( max

i i i b

b b u

i



*

b

* * *

( , ) ( , ),

i i i i i i i

u b b u b b b

 

  

utility company: deficit d customer i:

) , ( max

i i i b

b b u

i



Nash equilibrium

Theorem (Li, Chen, Dahleh, 2015) False cost

> 0

Efficiency Loss

Ratio of game cost over optimal cost

Question: Is there a way to make individuals report truthful information?

Human Incentive:

Strategic behavior, self-interested, market power Supply function bidding: Efficiency loss from strategic behavior

Power Engineering:

Power flow, system dynamics, operation constraints Markets efficiently allocate delivery costs to individuals (transactions)

Uncertainties:

Renewable energy, user’s behavior, emergency

This Talk: Electricity Market in Distribution Networks

Human Incentive:

Strategic behavior, self-interested, market power Supply function bidding: Efficiency loss from strategic behavior

Power Engineering:

Power flow, system dynamics, operation constraints Markets efficiently allocate delivery costs to individuals (transactions)

Uncertainties:

Renewable energy, user’s behavior, emergency

This Talk: Electricity Market in Distribution Networks

Recall: Supply Function Bidding

• A supply deficit d
• Customer i reduced load: qi
• Customer i reports a supply function (SF)
• Cost function of load shedding

customer 1: p

1

b

1 1

q b p  customer n:

n n

q b p  p

n

b utility company: deficit d

) (

i i q

C

Recall: Supply Function Bidding

• A forecasted supply deficit d in the future
• Customer i reduced load: qi
• Customer i reports a supply function (SF)
• Cost function of load shedding in the future

customer 1: p

1

b

1 1

q b p  customer n:

n n

q b p  p

n

b utility company: deficit d

) (

i i q

C

Caution: The information is uncertain! Challenge: How to guarantee reliability?

Incentivizing Reliability in Demand Response

A group of customers:

• are able to reduce loads, e.g., 2‐4pm in the next day

A reliability target:

• e.g. 1000 kW can be reduced with probability 99%

Challenges:

• Costly to reduce loads
• Uncertainty in the cost and ability to respond

Current practice (e.g., PJM, Con Edison, SCE, etc ):

• Enlisting large number of consumers,
• Offering rewards in an order based on experience
• Unguaranteed reliability as customers opt out in the process

Tw o Period Mechanism Time 0 Time 1

Agents report with knowledge

• f type (Ci)

Mechanism selects agents to prepare for reducing loads and determines rewards Ri, penalty Qi Agents resolve uncertainty in ability to respond Agents decide

• n responses,

if possible Mechanism pays rewards and collects penalties

Uncertain, Random Cost

Fixed Rew ard R Mechanism

• Mechanism computes agent maximum acceptable penalty Mi
• Select customers in decreasing order of Mi until reliability target is met
• Calculate critical payment Qi as penalty for non‐response

Theorem [Ma, Robu, Li, Parkes, 2016]: If the reward R is large enough, both direct and indirect mechanism guarantee truthful telling, individual rationality, and the reliability target.

Direct Mechanism Indirect Mechanism

• Agents reports their maximum acceptable penalty Mi

• First Best: suppose individual uncertainty is available; select to
• ptimize the reliability
• n = 500, M = 100, fix R = 10 or reliability τ = 98%

Direct, Indirect Vs. First Best

Conclusion and Discussion Human Incentive:

Strategic behavior, self-interested, market power Supply function bidding: Efficiency loss from strategic behavior

Power Engineering:

Power flow, System dynamics, operation constraints Markets efficiently allocate delivery costs to individuals (transactions)

Uncertainties:

Renewable energy, user’s behavior, emergency Mechanism design to ensure reliability

Challenge and future work: A market: takes account of engineering and human factors, achieves (sub)‐optimal efficiency, and ensures reliability

Research Interest Network Optimization, Control, Economics

Sensor Network

Distributed/Local Control Laws Desired Global System Behavior

Design general theories and tools for:

Transportation Internet network Parallel computing Social network Etc… Power Systems Data Center

Research Interest Network Optimization, Control, Economics

Sensor Network Transportation Internet network Parallel computing Social network Etc… Power Systems Data Center

Foundational Theories

Practical Algorithms Real Implementation

• Comm./Comp.

complexity

• Tradeoff between

efficiency, robustness, computation, and communication

• Optimal first‐order

distributed methods

• Regularized methods
• Physical

measurement‐aid algorithms

• Distributed power

capping in data center

• Microgrid energy

management

Acknowledgment :

Caltech: Steven Low MIT: Munther Dahleh

• Univ. of Colorado, Boulder: Lijun Chen

KTH: Sindri Magnusson, Carlo Fishchione Energy Trading Analytics: Hung‐po Chao Harvard Univ: Vahid Tarokh, David Parkes, Guannan Qu, Masoud Badiei, Yingying Li, Ariana Minot, Xuan Zhang, Chinwendu Enyioha, Hongyao Ma Funding Agencies: NSF, ARPA‐E