power market participation of flexible loads and reactive power...

Power Market Participation of Flexible

Loads and Reactive Power Providers: Real

Power, Reactive Power, and Regulation

Reserve Capacity Pricing at T&D Networks

DIMACS, Rutgers U

January 21, 2013

Michael Caramanis

[email protected]

2

Outline

• How can Flexible Loads Provide Fast Reserves

• How do Distribution Network Injections Differ From Transmission System Bus Injections?

• Current Market Bidding Rules Motivate Flexible Distributed Loads to Exercise Strategic Behavior Resulting in a Hierarchical Game

• Conditions for Hierarchical Game to Converge

• Revised Bidding Rules Remove Strategic Behavior Incentives and Allow ISO/“DNO” to Clear Market in a Socially Optimal Manner

• Detailed Distribution Market Pricing Real and Reactive Power

3

Outline

• How can Flexible Loads Provide Fast Reserves






4

Characteristic Generation Demand

Dispatchability-

Schedulability

Low/Med/High

Wind, Run of Riv /Neuclear,

L.E.P,/ HydroFossil

Capacity Loads, dependent on

env. e.g.,Light/ Ind. Energy

Loads Aluminum

idle/Schedulable production of

electr. energy intensive storable

products (gas liquif.)

Flexibility

Low/med/high

No Ramp – steady output

e.g., nucl, min gen, start up

cost and delay/ Inertia and

medium storage/high ramp-

low inertia large storage

Thermal or work inertia (Allum.

Smelter)/Enegy Demand with

small storage to capacity ratio

(HVAC)/ Large storage to

capacity ratio (ice, molten salt,

batteries in Evs)

Forecastaility

Low/Med/High

Wind, Solar. RoR

Hydro/reliable

fossil/unreliable fossil

Inflexible loads (lighting

cooking)/Weather

dependent/scheduled loads

Voltage Control Synchronous Generators with

dynamic Var compensators,

DC-AC Converters

Distributed Power Electronics

accompanying EVs. HVAC,

Roof top PV.

Generation and Demand Share Functional Characteristics that are

Key to the Efficient and reliable Operation of the Electricity Grid

5

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

D: 10/1/11

S: 9/1/10

Instance of PJM Regulation Signal, y(t). Note Constant Average over relatively

short period of Time

Flexible Loads Require Energy by some deadline =>

Capable of Regulation Reserves

6

Example of Generator providing Super Fast Reserves: Frequency control and 40MW of

Secondary Reserves

Source: Courtesy of EnThes Inc., March 2007

Today Generating Units are Only Reserve Providers

Frequency Control

Secondary Reserves

320MW50MW

7

Outline • How can Flexible Loads Provide Reserves






Distribution Network Low Voltage Bus Marginal Cost Based

Dynamic Prices (DLMP) Result from Augmenting Transmission

System High Voltage Prices (LMP) by Marginal cost of: Line

Losses, Reactive Power, Voltage control, Transformer Life Loss

8

HV, Bus n

LV, n(k) LMP at Bus n

DLMP at n(i)=mn(i)(LMP at n)+…Where mn(i)=(1+ML at n(i))…

LV, n(i)

9

Outline

• How can Flexible Loads Provide Reserves






Examples of Flexible Loads: State

Dynamics Determine Preferences

10

• Distributed PHEV Charging

• Centralized Pumped Storage Hydro Units

1

( ) ( ) ( ) ( )

dep time

( )

ˆ

0

j j j j

j

F F F F

F

t t t t

n i n i n i n i

n i

x x d

x

1

( ) ( ) ( ) ( ) ( )

0 2

( ) ( ) ( )

)

4

( ( )

psh psh t g t r R t

n p n p n p

ps

t t p

n p n p n

h

p n p n

p

p

n p p

h

n

s

x x p g g

x x

11

Strategic Flexible PHEV Load Behavior

, ( )( ) ( )

,

( ) ( ), ,

,, , ,

,

( ) ( ) ( ) ( )

1

( ) ( ) ( ) ( )

( ) ( )

{ [ λ

λ ] ( )}

. .

ˆ e.g., state dyn of EV dem.

min

j j

j

E t R t tF F R n n n it tj j

n i n i

j

j j j j

j j

F F

F F F F

F F R

Ft E t t

n i n n im

j td d j t

F Rt R t t t t

n i n n i n i n i

t t t t

n i n i n i n i

t t

n i n i

E m d

m d U x

s t

x x d

d d

λ λ

,

( ) ( ) ( )

up/dn nature of Reg. Res.

ˆ[ ] Local Constraintj jF F Rt t t

n i n i n i

j

d d C

Use of Current Bidding Rules to

Self Schedule

12

,* *

( ) ( )

, *

( ) ( )

Bid Energy at a very high price

Bid Energy 2 at energy price ~ λ

and Regulation Service Rate at 0.

j j

j

F F Rt t

n i n i

F R t t E t

n i n i n

d d

d m

Using the Current Bidding Rules. Bids described on the previous

slide, induce the ISO/DSO to almost surely Schedule Energy and

Reserves to the * values, and thus effectively self dispatch.

13

( ) ( ) ( )

*

( ) ( ) ( )

( ) ( ), ( )

,

( )

( )

( ) ( ) ( ) ( ) ( ) ( ), , ,

, ,

( ) * 2

( )

, *

( ) ( )

( ) , ( )

. .

0,

max

( )2

( )

j

c t t R tn i n n

j

j

c c R

Ft t c t

n n i n i

n n i j n i

c t E u t

n i n

n i

t t t t t t

n i n i n n n nd g g t

t i

Fn i t

n i

j

F RR t t

n n i

n j n i

s t

g d d

d t

u d c g r g

d

g d

,

( )

( )

& other capacity and ramp constr. for conv. gen. and dem.

R u t

n

c t

n i

n i

tLoss R

14

Outline







Hierarchical Game Dynamics

• Undamped Oscillations when Flex Load

Updates Clearing Price Estimates

Myopically to Most Recent ex-post

ISO/DMO value

• Convergence to stable equilibrium when

Flex Load Updates Clearing Price

Estimates Factoring in History, for

example sets them Equal to their Time

Average 15

16

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

1 5 91

31

72

1 25 29

33

37 41 45

49

53 57 61

65

69 73 77

81

85 89 93

97

101

105

109

113

117

121

125

129

133

137

141

145

149

153

157

161

165

169

173

% C

on

verg

en

ce

Iteration

UPQB LMP Convergence by Iteration (No Congestion)

Base Case

Discrete Smooth Case

Quadratic Case

17

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

1 5 913 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

101

105

109

113

117

121

125

129

133

137

141

145

149

153

157

161

165

169

173

% C

on

verg

en

ce

Iteration

UPQB LMP Convergence by Iteration (With Congestion)

Base Case Bus 1

Discrete Smooth Case Bus 1

Quadratic Case Bus 1

18

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

1 5 913 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

101

105

109

113

117

121

125

129

133

137

141

145

149

153

157

161

165

169

173

% C

on

verg

en

ce

Iteration

Step Size Impact on UPQB Convergence

Discrete Smooth Case Bus 1 (Steepest Descent)

Discrete Smooth Case Bus 1 (Averaging)

Quadratic Case Bus 1 (Steepest Descent)

Quadratic Case Bus 1 (Averaging)

19

(0.50)

(0.40)

(0.30)

(0.20)

(0.10)

-

0.10

0.20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

$/M

Wh

Hour

(UPQB LMP - TCCB LMP) by Iteration

Bus 1 Iterations 148, 151, 154, etc



20

Outline







Under New Bidding Rule allowing Flex Load to Express True Utility, ISO/DNO will Solve

21

,

( ) ( ) ( ) ( ) ( ) ( )

( )

( ) ( ), , , , , , , , , ,

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

( ) ( ), ( )

( )

( )

[

( )] . .

( )2

maxF F Rc t t R t t t W tj j

n i n n n i n i n

j j

j

j

c c

F FR

c t

n i

t t

n i n id g g d d g t i t

t t t t t t

n n n n n i n i

Ft t c t

n n i n i

n n i j n i

Fn i t

n i

j

d

u d

c g r g U x s t

g d d

d

( )

( )

( )

2 ,

( ) ( ) ( )

( ) ( ), ( )

( ) 2 ,

( )

1

( ) ( ) ( ) ( )

0,

( ) 0,2

ˆ ( ) Flex Load Dynamics

& other Local ( ) and System constrai

j

j

j j j j

n i

c t

n i

n i

F F F F

E x t

n

Ft t c t

n n i n i

n n i j n i

Fn i t E x t

n i n

j

t t t t

n i n i n i n i

d

t

g d d

d t

x x d n i

n i

nts

Complex Bid ISO/DNO Market Clearing

Achieves Hierarchical Game Equilibrium

22

• Theorem:

– First order Optimality Conditions

– Complementary Slackness, and

– Feasibility Conditions

Coincide if we combine Hierarchical game

problems and compare to ISO/DSO problem,

Except when Flex loads dominate in a Distr.

Location (competitive assumption fails?)

( )( ) ( )

, , ,

( ) ( ) ( ) () )

( )

,

(

£ 1

0

( )( )j

tn

Fji

j

F E t

ISO nd

R

c t

t t t j t j t

n n i n i n i

t

n i n i n i

j

F R t

n i n i

d d

d

Additional term in ISO/DNO problem

23

( )( ) ( )

, , ,

( ) ( ) ( ) () )

( )

,

(

£ 1

0

( )( )j

tn

Fji

j

F E t

ISO nd

R

c t

t t t j t j t

n n i n i n i

t

n i n i n i

j

F R t

n i n i

d d

d

( )

( ) ( )

,

Becomes negligible, i.e. 0 as

0

or as the relative size of flex load Reg. Res. Transactions 0

j

j

t

n i

t c t

n i n i

F R

F

d

d d

24 (250)

(200)

(150)

(100)

(50)

-

50

100

(0.40)

(0.30)

(0.20)

(0.10)

-

0.10

0.20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

$/M

Wh

$/M

Wh

Hour

Impact of Competitiveness Assumption

UPQB Price Spread - TCCB Price Spread

UPQB IFL Costs - TCCB IFL Costs

Conclusion • Flexible Loads at Distribution Level may

participate in Expanded ISO/DNO Centrally

Cleared Power Market bringing significant

benefits, particularly w.r.t. Sustainable

Renewable Generation Integration to the Grid

• Expanded ISO/DNO-Operated Power Market

Clearing is Practical from Information and

Computational Tractability Point of view.

• Inclusion of Other Important Distribution Network

Costs, such as Reactive Power Compensation

and Voltage Control is also Practical. 25

26

Outline







Ex. of Var. Speed HVAC - PV Collaboration:

Action in the small by Distr. Flex. Loads

27

Load and Other Resources May Participate fully in

Future Distribution Markets:

28

Centralized Dispatchable Generation Distributed Consumers

Centralized Non-Dispatchable Generation Distributed Generation

e.g., Wind Parks

Centralized Prosumers (e.g., cogeneration) Distributed Prosumers

Current market: Only Centralized generation is a full market participant. All others communicate their

capabilities and needs without feedback and response

Market

Centralized Dispatchable Generation Distributed Consumers

Centralized Non-Dispatchable Generation Distributed Generation

e.g. Wind Parks

Centralized Prosumers(e.g., cogeneration) Distributed Prosumers

Future Market: Many more non-dispatchable cedtralized generators, distributed generators and prosumers.

On the distributed side, “feedback” renders Non-Dispatchable generation and distributed consumers-

producers (prosumers) full market participants

Market

29

Example of a Radial Distribution Network: One Medium Voltage Branch is Shown

with three feeders, each with three building loads. Substation is the Slack Bus

Distribution Market Problem formulation: Minimize Utility Loss, Real and React. Power Cost (incl Losses), Asset Life

Loss, and Volt. Control Cost s.t. Load Flow , Capac., Volt. Magnitude Const

, ,

, ,

22 2

, , (1) , (1) 1m n m ni i i

i M M

m n m n

f fg d dP P P V

g m m m m b b

m i i f f

tMc P u P P C C Q c V

Minimize

Subject to

30

Distribution Market Problem formulation (cont.)

31

,

,

, , ,

,

2

1, 2, , ,

15000 15000exp ,

383 273

,

,

0

b m

b m

b m b m b m

f b mH

f

H A

f f f b m b m

b b b

f

k k S f

V V V b

A

Distribution Market Benefits • Marginal Losses Reflected in DLMPs=>Demand

Adaptation

• Reactive Power Pricing motivates Dual Use of

Power Electronics whose presence is expected to

Become Ubiquitous while accompanying

Distributed Clean Generation (e.g., PV)

installations and Flexible Loads (e.g., EVs, Heat

Pumps)

• Marginal Voltage Control Cost Reflected in DLMPs

=>Demand Adaptation

• Distribution Asset Degradation Marginal Costs

Reflected in DLMPs =>Demand Adaptation

• Full Distr. Net Price Unbundling =>Distr. Net Rent 32

power market participation of flexible loads and reactive power...

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