Fundamentals and Advances in Enterprise- wide Optimization...

Fundamentals and Advances in Enterprise-wide Optimization for Industrial Demand Side Management

EWO Seminar at CMU, Pittsburgh May 11, 2016

Qi Zhang

Center for Advanced Process Decision-making Department of Chemical Engineering, Carnegie Mellon University

The main driver for DSM is time-sensitive pricing

Electricity prices change on an hourly basis (more frequently in the real-time market)

Challenge, but also opportunity for electricity consumers

Hourly electricity prices in 2013

Time [h]

Pric

e [$

/MW

h]

Source: PJM Interconnection LLC

Chemical plants are large electricity consumers → high potential cost savings

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Outline

Part I: Fundamentals of deregulated electricity markets

• Power system economics

• Demand side management

Part II: Enterprise-wide optimization for industrial DSM

• Modeling operational flexibility

• Integration of production and energy management

• Multiscale decision-making

• Optimization under uncertainty

Conclusions

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Deregulated electricity markets involve many participants

An independent system operator (ISO) controls the transmission network and operates the wholesale market. Its primary responsibility is to ensure the reliability of the power grid.

Generation Transmission Distribution Consumption

Generating Companies

Transmission Companies

Retailers Small Consumers

Large Consumers

Distribution Companies

Wholesale Market

Retail Market

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In most parts of the U.S., electricity markets are deregulated

The U.S. is divided into 3 interconnected power grids

Deregulated electricity markets are operated by 7 ISOs and regional transmission organizations (RTOs), which are non-profit organizations

Source: AIChE CEP

Western Interconnect

Texas Interconnect

Eastern Interconnect

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Electricity is traded as a commodity and as a service

Balance between supply and demand must be maintained at all times

Electrical energy is very difficult to store

No lead time, electrical energy has to be produced at the same time it is consumed

Electrical energy market

• Electricity is treated as a commodity

Ancillary services market

• Backup capacities provided by flexible resources that can help eliminate supply-demand imbalance

• Categorized according to the response time, e.g. regulation (seconds) and operating reserves (minutes)

Ancillary services ensure grid reliability, but at the cost of reduced efficiency.

Power Generation

40 MW traded as ancillary services

50 MW traded in the energy market

Actual amount of power generated: 50-90 MW

50 MW

90 MW

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Electricity is traded through bilateral contracts and auctions

Bilateral contracting

• Buyer and seller enter into contracts without the ISO’s involvement

Auctions in electricity pools

• Electrical energy is indistinguishable

• Pooling results in economies of scale

• Generating companies submit bids ranked in order of increasing price

• Consumers submit offers ranked in order of decreasing price

• Market is cleared at the price where the constructed supply and demand curves intersect

After the market is cleared, the same price applies to all participants.

Quantity (MWh)

Price ($/MWh)

Supply

Demand

𝑃∗

𝑄∗

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Transmission constraints lead to locational marginal pricing

May 4, 2016, 14:00 May 4, 2016, 14:15

Source: MISO

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Modern power system operation is increasingly leveraging consumers’ load adjustment capabilities

The power grid is experiencing increased load variability and uncertainty due to growing demand and share of intermittent renewable power generation

Increased focus on DSM creates opportunities for power-intensive industries.

Net Load Curves Source: CAISO Demand side management (DSM) can help flatten the

net load curve

DSM is encouraged by financial incentives

Win-win for grid operator and consumer

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Classification of DSM activities

Demand Side Management

Energy Efficiency (EE) Demand Response (DR)

Dispatchable DR Nondispatchable DR

Process Design/Retrofit

Load Profile Adjustment in Response to Price Changes

Load Profile Adjustment in Response to DR Events

Direct Load Control

Interruptible Load

Ancillary Services

…

Time-of-Use Pricing

Critical Peak Pricing

Real-Time Pricing

…

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Outline









Conclusions

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We identify four major challenges in industrial DSM

iDSM

Modeling Process Dynamics and

Operational Flexibility

Integration of Production and

Energy Management

Decision-making Across Multiple

Time and Space Scales

Forecasting and Optimization Under

Uncertainty

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Incorporating time-varying prices into discrete-time models is straightforward, not so in continuous-time formulations

Discrete-time models may require a large number of time periods

Continuous-time models may be smaller but tend to be more complex

For example, MILP constraints can be formulated to consider the following task-interval overlap cases1,2:

Case 1

Price Interval

Case 2

Case 3

Case 4

Case 5

Case 6

Time

Task: Overlap:

1. Nolde & Morari (2010). Computers & Chemical Engineering, 34(11), 1899-1903. 2. Hait & Artigues (2011). Computers & Chemical Engineering, 35(12), 3044-3047.

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Incorporating time-varying prices into discrete-time models is straightforward, not so in continuous-time formulations

Alternatively, continuous time representation can be applied by disaggregating each task into tasks executed at different electricity prices1:

Arrive at the following MILP constraints:

Task A-E2 Task B-E1 Task B-E2

Cost E2 Cost E1 Cost E2 Cost E3

Time 𝜏𝑡

𝑈𝐸𝐸,𝑝−1 𝐿𝐸𝐸,𝑝

𝑈𝐸𝐸,𝑝 𝐿𝐸1,𝑝

𝑈𝐸1,𝑝 𝐿𝐸𝐸,𝑝

𝜏𝑡+1 𝜏𝑡+𝐸 𝜏𝑡+𝐸 �̂�𝑡 �̂�𝑡+1 �̂�𝑡+𝐸

Discrete-time models show better computational performance in large problems.

1. Castro et al. (2009). I&ECR, 48(14), 6701-6714.

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Constraints on operational transitions can be formulated in a mode-based MILP scheduling model

Off Startup On after 4 hours after at least

24 hours

after 2 hours Shutdown

after at least 12 hours In each time period, the plant can only operate in one mode:

Modeling transitions: Tighter formulation with fewer constraints1:

Fewer variables and constraints by eliminating self-transitions2:

1. Sahinidis & Grossmann (1991). Computers & Chemical Engineering, 15(4), 255-272. 2. Mitra et al. (2013). Energy, 54, 194-211.

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A large variety of power contracts can be modeled using a block contract formulation

Electricity Purchase [kWh]

Uni

t Pric

e [$

/kW

h]

𝛽1

𝛽𝐸

𝛽𝐸

𝐻1max 𝐻𝐸max

Pena

lty [$

]

𝐻1max 𝐻𝐸max

𝑏 = 1 𝑏 = 2 𝑏 = 3

Electricity Purchase [kWh]

Formulated using the following disjunction1: Discount contract:

Penalty contract:

1. Z. et al. (2016). Computers & Chemical Engineering, 84, 382-393.

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Industrial Case Study 1 Deterministic scheduling of an air separation plant1

AS

VentGO2

LMCompGN2

DrioxO2

DrioxN2

MPGN2

VGO2 VGN2

GO2

LO2

LN2

GN2

LAr

LiqGN2

VentGN2

LHCompGN2

MHCompGN2

HPGN2

VMPGN2

VentMPGN2

VentMPGN2

VHPGN2


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Industrial Case Study 1 Optimize the production schedule over an entire week

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

Elec

tric

ity C

onsu

mpt

ion

AS LiqGN2 LMCompGN2 MHCompGN2 LHCompGN2

0

20

40

60

80

100

018003600540072009000

1080012600

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

Elec

tric

ity P

rice

[$/M

Wh]

Elec

tric

ity P

urch

ase

Time of Use Contract Spot Market Penalty Contract Time of Use Price Spot Price Penalty Contract Price

Time [h]

Time [h]

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Industrial Case Study 1 Storage capacity allows flexibility for load shifting

Main advantages of the model: proper modeling of operational transitions and computational efficiency (solves within a minute)

Model size: 28,808 cont. var., 9776 bin. var., 113,810 cons.

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ntor

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vel

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When making long-term decisions, also the short-term effects due to time-sensitive pricing have to be considered

An hourly time discretization over the entire length of the planning horizon (e.g. a year) is computationally intractable

To capture the seasonal behavior of electricity prices, the planning horizon is often divided into seasons with each season represented by one or more characteristic weeks1

Week Sp1

Week Sp2

Week Su1

Week Su2

Week Fa1

Week Fa2

Week Wi1

Week Wi2

Spring Summer Fall Winter

1. Mitra et al. (2014). Computers & Chemical Engineering, 65, 89-101.

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Outline









Conclusions

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Electricity price uncertainty is often modeled using two-stage stochastic programming1

Uncertainty characterized by a set of scenarios with given probabilities

Often scenario reduction and decomposition methods are required to achieve computational tractability2

1. Birge, Louveaux (2011).

Scheduling horizon

Here-and-now decisions

Wait-and-see decisions

Time

Elec

tric

ity P

rice


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DSM allows participation in the ancillary services market

Supply Demand

Supply Demand

Supply Demand

Shortage of supply compensated by generators with short ramp-up times

Referred to as operating reserve Expensive, requires underutilization of

generation facilities

Supply-demand mismatch eliminated by reducing electricity consumption

Also referred to as interruptible load Less expensive, reduces the need of

building new power plants

<

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Dispatchable DR is subject to high uncertainty

Target power consumption

Minimum power consumption

Time

Power Consumption

Interruptible Load

Load reduction requested

Load reduction requested

Actual power consumption

Load reduction demand is uncertain

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Apply adjustable robust optimization approach to incorporate recourse decisions1

Decisions have to depend on the realization of the uncertainty

Traditional static robust optimization: No recourse, only here-and-now decisions

Adjustable robust optimization2: Recourse decision variables are specified as functions of the uncertain parameters

For tractability reasons, restrict to affine functions:

1. Z. et al. (2016). Computers & Chemical Engineering, 86, 106-119. 2. Ben-Tal et al. (2004). Mathematical Programming, 99(2), 351-376.

actual production

target production

uncertain load reduction

decision coefficient

multistage linear decision rule

𝑝𝑡 and 𝑞𝑡𝑡 are decision variables 𝜁 defines the extent of recourse

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Robust solutions are found with respect to a given uncertainty set while minimizing the worst-case cost

MILP Model:

minimize electricity cost + product purchase cost - interruptible load sales

subject to surrogate process model mass balances energy balances mode transition constraints initial conditions terminal constraints

for all possible realizations of the uncertainty, i.e. ∀ 𝒘 ∈ 𝑾(𝑰𝑰)

max( )

interruptible load provided

load reduction demand

normalized load reduction demand

budget parameter

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Industrial Case Study 2 Without interruptible load, try to avoid high-price periods

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160

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Pric

e [$

/MW

h]

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tric

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onsu

mpt

ion

Time [h]

Target Electricity Consumption Electricity Price

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LO2

In a

nd O

ut F

low

s

LO2

Inve

ntor

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vel

Time [h] LO2 Production LO2 Purchase LO2 Demand LO2 Inventory

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40Final inventory level reaches the minimum

(= initial inventory)

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Industrial Case Study 2: Interruptible load reduces total operating cost, even with minimum extent of recourse (𝜻 = 𝟎)

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Provided Interruptible Load Target Electricity Consumption Electricity Price Interruptible Load Price

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LO2

Inve

ntor

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vel

Time [h] Target LO2 Production Target LO2 Purchase LO2 Demand Production Recourse Purchase Recourse Target LO2 Inventory

1.2% cost savings (worst case)

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Inventory buffer built to ensure

feasibility

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Industrial Case Study 2: Cost savings increase by 50% if greater extent of recourse is considered (𝜻 = 𝟐𝟐)

1.8% cost savings (worst case)

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160

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mpt

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Time [h] Provided Interruptible Load Target Electricity Consumption Electricity Price Interruptible Load Price

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LO2

In a

nd O

ut F

low

s

LO2

Inve

ntor

y Le

vel

Time [h] Target LO2 Production Target LO2 Purchase LO2 Demand Production Recourse Purchase Recourse Target LO2 Inventory

No inventory buffer required

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Outline









Conclusions

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Conclusions

Win-win: DSM increases power grid performance as well as consumer benefits

Need basic understanding of electricity market mechanisms

EWO can help maximize benefits from DSM for power-intensive industries

Future opportunities:

• Consider collaboration between companies operating interrelated power-intensive processes, e.g. steel plant and air separation plant

• Consider DSM at the supply chain level

• Optimize bidding strategy for large consumers

• Explore more dispatchable DR opportunities

• Co-optimize production scheduling, energy management, and energy trading

• Develop more efficient algorithms to solve larger problems (multiscale, stochastic)

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References

Kirschen, D. & Strbac, G. (2004). Fundamentals of Power System Economics. John Wiley & Sons, Ltd.

Zhang, Q. & Grossmann, I. E. (2016). Planning and Scheduling for Industrial Demand Side Management: Advances and Challenges. In: Martin, M. (Ed.), Alternative Energy Sources and Technologies: Process Design and Operation (pp. 383-414), Springer.

Zhang, Q. & Grossmann, I. E. (2016). Enterprise-wide Optimization for Industrial Demand Side Management: Fundamentals, Advances, and Perspectives. In preparation.

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Fundamentals and Advances in Enterprise- wide Optimization...

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