analysis and control design of sustainable policies for...

SusTEM 2011 Newcastle

Analysis and Control Design of

Sustainable Policies for Greenhouse Gas

Emissions

Bing Chu1, Stephen Duncan1, Antonis Papachristodoulou1

and Cameron Hepburn2,3

1 Department of Engineering Science, Oxford University, UK

2 Smith School of Enterprise and the Environment, Oxford

University, UK 3 Graham Research Institute, London School of Economics, UK


Introduction and Motivation

UK 4see Model and Simulink Implementation

Preliminary Analysis Results

Model Predictive Control

Conclusion and Future Work

Outline


Climate Change and GHG Reduction

Global Warming needs urgent

action to reduce Greenhouse

Gas (GHG) emissions

UK GHG Reduction

Target :

34% by2020

80% by2050


Using Control Theory for Policy Design

CO2

GDP

Employment

……

Sustainable Policies

Emissions Target

2010 2020 2030 2040 2050 2060 20701

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6x 10

8

time(year)

CO

2 g

enera

ted index (

tonnes C

O2/y

r)

CO2 generated index


Requirement for Determining Policies

To apply control, need

Specification for desired future behaviour of system

Emissions targets up to 2050

Method of changing for changing state of system

Actuators

Policies (mix of electricity generation, electric vehicles …)

Method of predicting future effect of applying input signal to

actuator

Model of system’s behaviour


Using Control Theory for Policy Design

CO2

GDP

Employment

……

Sustainable Policies

Feedback Controller

Emissions Target

2010 2020 2030 2040 2050 2060 20701

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6x 10

8

time(year)

CO

2 g

enera

ted index (

tonnes C

O2/y

r)

CO2 generated index

+

-


Requirement for Determining Policies

To apply control, need

Specification for desired future behaviour of system

Emissions targets up to 2050

Method of changing for changing state of system

Policies (mix of electricity generation, electric vehicles …)

Method of predicting future effect of applying input signal to

actuator

Model of system’s behaviour

A sensor that takes a measurement of actual emissions

Compare actual emissions with target

Use error to adjust policies


The Benefit of Feedback

Handles uncertainty in a systematic manner

Makes system robust to

Model uncertainties (model parameters)

Disturbances (recession, cold winters, …)

Errors in measurements

BUT

An incorrectly designed feedback can make a stable

system unstable

Feedback must be designed correctly


Models for Sustainable Development

Variety of models for UK, e.g.

Centralized optimization models: e.g. MARKAL family

Computable general equilibrium models: e.g. GEM-3

System dynamics models: e.g. UK 4see

UK 4see model:

Based on general system theory

Convenient structural properties

Chosen as a test bed for our design approach.


4see Model for the UK

Evolution of Capital Creation Options (ECCO) is a

high level macroeconomic modeling methodology

1. Identify the main sectors

Crane, 1996

2. Fit the parameters


UK 4see Model: VenSim Version

2 2 2

2

RF CO CO released by oil CO released by gas

CO released by coal

d( )

d

Nuclear generating capacityrate of building Nuc

t

rate of depreciation Nuc

rate of decommissioning of Nuc

13 sectors, 946 equations


UK 4see: State Space Formulation

The UK 4see model can be expressed in form

x: system states (e.g. capital stock of industry)

u: system input (e.g. energy policies)

v: the auxiliary (algebraic) variables

y: system output (measures of interest e.g. CO2 emissions

and economic index)

),,(

),,(0

),,(

vuxgy

vuxh

vuxqx


Simulink Implementation

VenSim’s functionality is limited for the purpose of

control systems design Simulink


2000 2005 2010 2015 2020 20254

4.2

4.4

4.6

4.8

5

5.2

5.4

5.6

5.8

6x 10

8

time(year)

CO

2 g

enera

ted index (

tonnes C

O2/y

r)

2000 2005 2010 2015 2020 20251

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

index m

ate

rial sta

ndard

of

livin

g p

er

capita

CO2 generated index

index material standard of living per capita

Simulation Results for ‘BAU’ Case

Simulation results under ‘business as usual’ policies

UK 2020 Reduction Target:

391.4 millions tonnes/year

(34% cut)

Need for a sustainable

policy design


2000 2005 2010 2015 2020 20254

4.2

4.4

4.6

4.8

5

5.2

5.4

5.6

5.8

6x 10

8

time(year)

CO

2 g

enera

ted index (

tonnes C

O2/y

r)

2000 2005 2010 2015 2020 20251

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

index m

ate

rial sta

ndard

of

livin

g p

er

capita

CO2 generated index


UK 4see model is nonlinear

UK 4see: Linearised Model

Linearise at year

t = 2010

Simulation results under ‘business as usual’ policies

41 61 2, ,

x Ax Bu

y Cx Du

x R u R y R


Validation of the Linearised Model

CO2 Emissions: Comparison of responses for

the nonlinear and linearised models

2000 2005 2010 2015 2020 20254

4.2

4.4

4.6

4.8

5

5.2

5.4

5.6

5.8

6x 10

8

CO

2 g

enera

ted index (

tonnes C

O2/y

r)

CO2 generated index

original response

response with added step test signal

response of linearised model with step test signal


Linearized Model is Unstable

The system has

an unstable pole

at s = 0.014

All the sectors

are stable

Why?

Figure: Pole-Zero map of the linearized model


Structural Analysis of Linearized Model

Explore structure of system matrix A using graph theory

dwellings

services

agriculture

carbon

electricity

employment

global coef

industry

resource and mining

standard of living

transport

water

Identify the ‘underlying’ structure


Hierarchical Structure of Model Obtain hierarchical structure of system using energy

based method

dwellings services

agriculture

carbon

electricity

employmentglobal coef

industry

resource and mining

standard of living

transport water

Hierarchical structure of the linearized model. Upper sectors have significantly more effect on the lower sectors, while the effect of the lower sectors on the upper sectors is very small and can be neglected.

Strong feedback links

Instability


Formulation of Policy Design Problem

Design policies:

Achieve sustainable emissions of CO2

Minimise impact on economy

Optimal control Problem

uU set of policies including

investment in industry

fraction of vehicles powered by batteries

fraction of electricity produced by renewable energy

2011d),(minarg*

tUutuyfu

222

222),( baseu

BAUSOLSOLSOLCOCOCO uuryryuyf


Model Predictive Control Solution

Sequentially solving the following problem

Implementation

Use system model and x(t0) predict output y(t), t0 < t ≤ t0 + Np

Solve optimisation problem to obtain u*(t), t0 ≤ t < t0 + Nu

Implement the current input u*(t0) to the system

At next time step, repeat the above steps

A feedback control mechanism

pNt

ttUutuyfu

0

0

d ),(minarg


Choice of Reduction Trajectory

2010 2020 2030 2040 2050 2060 20701

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6x 10

8

time(year)

CO

2 g

enera

ted index (

tonnes C

O2/y

r)

CO2 generated index

2020: 34% cut

2050: 80% cut


MPC Design: Simulation Results

1990 2000 2010 2020 2030 2040 2050 2060 20701

2

3

4

5

6

7

8

9x 10

8

time(year)

CO

2 g

enera

ted index (

tonnes C

O2/y

r)

CO2 generated index

MPC

REF

BAU

CO2 Emissions until 2070 using MPC design



Economic growth as measured by index material standard of living per capita until 2070 using MPC design.

1990 2000 2010 2020 2030 2040 2050 2060 20701

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

time(year)

index m

ate

rial sta

ndard

of

livin

g p

er

capita


MPC

BAU



Fraction of electricity produced by renewable energy: MPC design

1990 2000 2010 2020 2030 2040 2050 2060 20700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

fraction S

renew

able

s

time(year)

fraction S renewables

MPC

BAU



Fractions of electrical cell vehicles : MPC design

1990 2000 2010 2020 2030 2040 2050 2060 20700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

fraction o

f ele

ctr

ical cell

vehic

les

time(year)

fraction of electrical cell vehicles

MPC

BAU


Conclusion and Future Work

Use feedback to reduce effect of model uncertainty

Parameter uncertainty, disturbances

The UK 4see model has been introduced and analysed

Design sustainable policy using feedback control theory

Model predictive control

Apply to other models

Analyse robustness to uncertainties

The behaviour of policy makers


Acknowledgements

Dr Simon Roberts

Arup Innovation

UK Engineering and Physical Sciences Research Council

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