a dynamic framework for real time and regulation for smart grids€¦ · actual generation and...

A Dynamic Framework for Real‐time and Regulation Markets for Smart Grids

Active‐adaptive Control LaboratoryDepartment of Mechanical Engineering

Massachusetts Institute of Technology

Anuradha Annaswamy

* Joint work with A. Kiani, J. Knudsen, J. Hansen, D. Shiltz, M. Cvetkovic, T. Nudell, N. Nandakumar

IMA Workshop on Control at Large Scales: Energy Markets and Responsive Grids

Paradigm Shift in Power Grids

Conventional Grid

Generation

Distribution Consumers

Distribution

Industrial Consumers

Transmission

NetworkOperations

NetworkOperations

Smart Meters

Transmission

Distribution

Smart Devices

DERs

Demand Response

Utilities

Microgrid

Industrial Consumers

Distribution Consumers

Distributed Community Storage

Energy providers

Generation Facilities

Increasing supply‐demand gap

Environmental concerns

Aging infrastructures

Two major changes:• Renewable energy resources• Demand Response

Control at Large Scales: Energy Markets, IMA Workshop, May 9‐13, 2016

Both necessitate a dynamic framework– Dynamic Market Mechanisms

Outline of my talk

• What is a Dynamic Market Mechanism?

• DMM and Frequency Regulation

• Dynamic Regulation Market Mechanisms

• Case study 1: 118 bus• Case study 2: 3120 bus• Case study 2: 3 interconnected 900‐bus


Focus is on wholesale markets

Economic Dispatch Today

Periodic with a regular interval.Single iteration process.Centralized computation.

Economic dispatch interval Time

Inflexible load

Generationset‐points

Automaticgenerationcontrol

Collect cost curves Find optimal dispatch Communicate set‐points

ISO

Flexibledemand

Generation


Dynamic Market MechanismOptimize social welfare

Subject to constraints

Lagrangian:

x: power generation/consumption :LMPsh: equality constraints :congestion pricesg: inequality constraints


( , )

0i l l jGc Gw w D nm n m

i l j n m

P P P B max

nm n m nmB P

j j i i l lW D D Gc Gc Gw Gwj i l

S U P C P C P

, , T TL x f x h x g x

, ,k k k kxx L x DMM: ‐ an iterative solution for economic dispatch

Dynamic Market Mechanism (DMM): An iterative solution

Economic dispatch interval Time


• Use recent information , ,• Cost curves · remain private

Inflexible load

Start negotiations

Negotiate and converge to an optimal solution

Implement set‐points


Sufficiently long period for convergence


: Power generation/consumption: Marginal price: Social Welfare incl. Marginal Cost: Equality constraints: Inequality constraints

, , T TL x f x h x g x

Δ , ,Δ , ,

DMM and Demand Response*Generation

(with Renewable Energy Resources)

Consumption

ISO

, : Suggested generation/consumption at time : Suggested price at time


Dynamic Market Mechanism (contd.)*

• Efficient – Unique Equilibrium under KKT conditions• Quantifies effect of volatility and stability• Can help reduce reserve costs with uncertainty Δ in renewables• Can incorporate adjustable DR ‐

* Kiani and Annaswamy, IEEE TSG, 2014

Simulation ResultsWind Properties:

: Actual Wind Power: Mean value of the projected wind. Current Market Practice: ARMA model of the actual wind power. With DMM

G

2 1

4 3 Area 2 Area 1

PD1PD2

G G

L1L2


Simulation Results: Effect of Wind Uncertainty*

Less reserve is required. Hierarchical coordination

* Kiani, Annaswamy, and Samad, IEEE TSG, 2014.


All consumption devices were assumed to be adjustable.

• Most flexible type of demand (can consume or supply power)

• Example: energy storage units, HVAC

• Have a deadline for achieving a fully charged state

• Example: Plug-in Hybrid Electric Vehicle

• Energy must be consumed in an uninterrupted stretch

• Example: industrial production cycles

Buckets PDc

Batteries PDt

Bakeries PDk

Source: J. Hansen, J. Knudsen, and A.M. Annaswamy, “Demand Response in Smart Grids: Participants, Challenges, and a Taxonomy,” IEEE CDC, Los Angeles, CA, 2015

Demand Response: Bucket, Battery, Bakery

The BBB Configuration

Nodal Power Balance

Line Capacity

Generation/Demand Power Limits

Generation Rates of ChangeDemand Energy Limits

Note:The index k corresponds with the market clearing instance

* J. Knudsen, J. Hansen, and A.M. Annaswamy “A Dynamic Market Mechanism for the Integration of Renewables and Demand Response,” IEEE Transactions on Control Systems Technology, vol. 24, No. 3, 2016.

Problem Formulation (including BBB)*

The index K corresponds with the negotiation iterations

The Overall DMM

Conventional generation

Renewable generation

Demand response

Voltage angles

• Stability and convergence can be guaranteed.

Modified IEEE 118 Bus Test Case*Bus consists of:• 45 conventional generators• 9 renewable generators (30% penetration)• 7 consumers (10% penetration)• 186 transmission lines


* Knudsen, Hansen, Annaswamy, IEEE‐CST, 2016

Results: IEEE‐118 bus


Outline of my talk• Dynamic Market Mechanisms for Wholesale Markets – an Introduction





DMM and shorter dispatch interval

Implement dispatch on shorter intervals.

Opportunities for addressing:o Significant and unpredicted

penetration of renewableso Non‐zero mean volatility of

renewable generationo High regulation requirements

in presence of renewables

Time


Economic dispatch interval


Inflexible load

Start negotiations

Negotiate and converge to an optimal solution

Implement set‐pointsSufficiently long period

for convergence


4

Time‐scales Introduced by DMM

DMM Negotiations

AGCUpdates

DMM Market Clearing

OPF Market Clearing

Existing time‐scales New time‐scales


Integrated DMM (economic dispatch + AGC)

Energy Market

Regulation Market

AutomaticGenerationControl

Assumption of magnitude and time‐scale separation between OPF and AGC.

Large penetration of intermittent energy represents a challenge.

Conventional architecture

Energy Market

Regulation Market

AutomaticGenerationControl

Aggregated feedback from AGC

Simultaneous decisions at both markets.

Proposed approach


DMM Iterates

• Augmented Lagrangian:

• Update x and using Newton’s method

2' '

2T cL f x h x h x

min. . ' 0

f xs t h x

-SW + Barrier Functions

Power Balance + KLB (ACE)m – 2

feedback gain

disaggregation matrix

ACE from measurement phase

1 ,

0 '

k kkx

k k

L xH NxN h x

Feedback from AGC to DMM

• Frequency measurements averaged over , are used in negotiations during , , which take effect during the operating period , .

Negotiations OperationMeasurements


DMM Iterates Final FormApproximated Hessian• Increases rate of convergence• Preserves privacy

Distributed gradient updates• A single cost/utility bid per iteration• Preserves privacy

· ·

· ·

Modified power balance• Integrates real‐time market and AGC• Includes disaggregated ACE error as an extra load on the buses• Market players can bid to optimally meet this load


* Shiltz, Cvetkovic, Annaswamy, IEEE Transactions on Sustainable Energy, vol. 7, No. 2, 2016.

′ )

Procedure:1. ISO sends xk2. Market players send f3. ISO computes and h’4. ISO computes xk+1

Modified IEEE 118 Bus Test CaseBus consists of:• 45 conventional generators• 9 renewable generators (30% penetration)• 7 flexible consumers (10% penetration)• 186 transmission lines


0 500 1000 15001400

1600

1800

2000

2200

2400

2600

Time [s]

Gen

erat

ion

[MW

]

0 500 1000 1500

245250255260265270275

Flex

ible

Dem

and

[MW

]

DMM Market Clearings (50 clearings)30 s

Conventional Generation

Renewable Generation

Flexible Demand


Negotiations over a single 30 second period

1110 1115 1120 1125 1130 1135 114022

24

26

28

30

32

34

36

Time [s]

Flex

ible

Con

sum

ptio

n [M

W]

1110 1115 1120 1125 1130 1135 11400

50

100

150

200

250

300

350

400

Time [s]Co

nven

tiona

l Gen

erat

ion

[MW

]

Conventional generation

Renewable generation

Demand response

Voltage angles


Actual Generation and Demand (With AGC feedback)

0 500 1000 15001400

1600

1800

2000

2200

2400

2600

Time [s]

Gen

erat

ion

[MW

]

0 500 1000 1500

245250255260265270275

Flex

ible

Dem

and

[MW

]

Conventional Generation

Renewable Generation

Flexible Demand


Impact on Area Control Error

• Peaks less severe using DMM than OPF• Adding feedback shifts ACE closer to zero


Summary of DMM (with AGC)*1. Allows flexible consumers to act as price‐setters at the

real‐time market (and not only to respond to price)

2. Admits the most recent weather predictions in market clearing (every 30 seconds)

3. Enables feedback from AGC layer into the market layer, reducing regulation requirements

4. Preserves privacy of market players’ sensitive information– e.g. cost curves, generation/consumption bounds

Is this scaleable?* Shiltz, Cvetkovic, Annaswamy, IEEE Transactions on Sustainable Energy, vol. 7, No. 2, 2016.


Number of iterations to convergenceMatpower test cases

The convergence time depends on:• Step size • Congestion• Cost curves

Number of iterations does not increase with decision variables


Polish 3120 Bus Test System

Data source:Matpower

Figure source:Paul Hines, “Estimating and Mitigating Cascading Failure Risk”, JST‐NSF‐DFG‐RCN Workshop, April 2015

The system consists of:• 3120 buses • 3693 transmission lines with line

capacities of 250 MW• 505 generators with linear cost curves

and capacities in the range 10MW‐150MW


Single DMM Clearing

30ms per iteration

=30 s

Transmission line flows Power generation

Locational marginal prices

Generation and price increase at bus 3010 once three transmission lines reach their limits.

Line 59congestion

Lines 31,32congestion


Outline of my talk• Dynamic Market Mechanisms for Wholesale Markets – an Introduction





Dynamic Regulation Market Mechanism• In frequency regulation, set‐points

are communicated every 2‐4 seconds

• DMM takes roughly 30 seconds to converge

• Can we use intermediate negotiations as set‐points?

t = 0 t = 30 s

PG


DRMM as Secondary Control• Current practice:

• Proposal:

Real Time Market

Secondary Control

Primary Control

Generator and DR set-point adjustments

Every 2-4 seconds

Wholesale dispatch

Every 5 minutes

Area Control Error

Real Time Market DRMM Primary

Control


Every 2-4 seconds

Wholesale dispatchEvery 5 minutes

Area Control Error

Price response signals

Market Players

Regulation Market

Once per hour


Primary Control Dynamics

• Bus dynamics (swing equation)

M

C

YPP

bus frequencies

bus voltage angles

governor valve positions

power generation

power consumption

G

D

Pu

P

commanded generation

commanded consumption

,

j j i

i i

i i i i M C L ij i j Gj j i j

M D P P P T i

G D E

N

,

j i

i

i i C L ij i j Lj i j

D P P T i

D E

N


: Buses with at least one generator:Load buses

Primary Control Dynamics (cont.)• Simplified generator model

• DR aggregator

• Combined dynamics

LA B u E P inflexible load(exogenous)

1i iG i G i j

i

Y P Y iR

Gdroop control

i i iCH M i MP Y P i G

i i i iD C D CP P P i D


Comes from the DRMM

DRMMPrimary ControlWholesale dispatch

Market Players

ACE

(governor)

(turbine)

DRMM Dynamics• Similar to DMM• Decision variables:

• Update Equations:

• Solves modified OPF:min fs.t. h = 0

g 0ED = 0

G

D

PP

commanded voltage angles

commanded generation

commanded consumption

1 1 ˆˆk k k khH N

price reply signalsnegotiated

prices at buses

“error‐like” signal

modified power balance (including frequency

feedback)

energy neutral requirement of DR


Link between Primary Control and DRMM

• Primary control:

• Assume PL and u vary slowly ≡

where

• Δ (ex. Δ 1

LA B u E P


1k k k kB E Lu P

A te 0

tA s

B e dsB

0

tA s

E e dsE

DRMM Implementation• Two way communication with System Operator

• Set‐point vector drives both physics AND market negotiations in real time

• Conditions for stability and frequency regulation can be derived.*

• * Shiltz and Annaswamy, American Control Conference, 2016


ControlWholesale dispatch

Market Players

ACE


Every 5 minutes Once per second

Generator and DR set-point adjustmentsPrice response signals

3‐area 900‐bus example• Extended to multiple interconnected power systems

– 3 Areas, 900 buses, 1233 transmission lines, 168 generators, 90 DR units


Disturbance Profile• Load imbalance occurs at t = 0• Load imbalance assumed to be restored (by RTM dispatch) as

shown in the figure


Results• Frequency and tie line flows restored in all three areas


Results (cont.)• Define regulation service costs as

• DR shifts consumption into the future, when the need for power is less


2W ACES S c ACE

Results (cont.)• Regulation costs can be significantly reduced if DR units are able

to defer consumption


costs normalized by the cost of primary control aloneenergy payback profiles

Summary• Dynamic Market Mechanism – A framework for Wind and Solar integration and DR.

• Two different DMMs outlined.• Dispatch DMM

– Economic dispatch can be made faster (~30s)– Aggregated feedback from AGC can be introduced to result in reduced ACE.

– Improvement in Social Welfare– Validation in 118 and 3120 buses

• Dynamic Regulation Market Mechanism– Market and frequency dynamics proceed at the same time‐scale

– Validation in a 3‐area 900‐bus networks


Dynamic Market Mechanism for Dispatch

Real Time Market

Secondary Control

Primary Control


Every 2-4 seconds

Wholesale dispatch

Every 5 minutes

Area Control Error

Regulation Market

Once per hour

Current Practice

Secondary Control

Primary Control


Every 2-4 seconds

Wholesale dispatch

Every 30 seconds

Area Control Error

Regulation Market

Once per hour

DMM

Market Players

Negotiationsseveral per second

DMM

Dynamic Regulation Market Mechanism for frequency regulation

• Current practice:

Real Time Market

Secondary Control

Primary Control


Every 2-4 seconds

Wholesale dispatch

Every 5 minutes

Area Control Error

Regulation Market

Once per hour



Control


Every 2-4 seconds

Wholesale dispatchEvery 5 minutes

Area Control Error

Price response signals

Market PlayersDRMM

References

• A. Kiani, A.M. Annaswamy, and T. Samad, “A Hierarchical Transactive Control Architecture for Renewables Integration in Smart Grids: Analytical modeling and stability,” IEEE Transactions on Smart Grid, Special Issue on Control Theory and Technology, 5(4):2054–2065, July 2014.

• A. Kiani and A.M. Annaswamy. “A Dynamic Mechanism for Wholesale Energy Market: Stability and Robustness”, IEEE Transactions on Smart Grid, 5(6):2877‐2888, November 2014.

• A. Kiani and A. M. Annaswamy. “Equilibrium in Wholesale Energy Markets: Perturbation Analysis in the Presence of Renewables”, IEEE Transactions on Smart Grid, 5(1):177–187, Jan 2014.

• Y. Sharon, A. M. Annaswamy, A. Motto, and A. Chakraborty, “Adaptive Control for Regulation of a Quadratic Function of the State,” IEEE Transactions on Automatic Control, 59(10):2831‐2836, October 2014.

• J. Hansen, J. Knudsen and A. M. Annaswamy. "A Dynamic Market Mechanism for Integration of Renewables and Demand Response,”, IEEE Transactions on Control Systems Technology, 2016.

• D. Shiltz, M. Cvetkovic, and A.M. Annaswamy, “An Integrated Dynamic Market Mechanism for Real‐time Markets and Frequency Regulation,”, IEEE Transactions on Sustainable Energy, vol. 7, No. 2, 2016.

• D. Shiltz and A.M. Annaswamy, “A Practical Integration of Automatic Generation Control and Demand Response“, American Control Conference, July 2016.


Come to the ACC, Boston!

• Smart Grid Control Workshop, July 5 2016

• Foundations of Infrastructure‐CPS, July 6 2016


THANK YOU!


a dynamic framework for real time and regulation for smart grids€¦ · actual generation and...

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