reliability and risk engineering

||

RREReliability and Risk Engineering

Andrea Antenucci and Prof. Giovanni Sansavini

Reliability and Risk Engineering Laboratory, D-Mechanical and Process Engineering, ETH Zurich

04.04.2019 1

Secure Allocation Of Power Reserves With Large Renewable

Penetration Under Gas Transmission Constraints

Giovanni Sansavini

||


04.04.2019Giovanni Sansavini 2

Why the Need for Coupling?

Beside power generation, gas-fired power plants

provide reserves to balance the volatility of

renewables

World net electricity generation by fuel [1012·kWh]

Renewables conversion into gas and network

storage can mitigate curtailments and

seasonality

International Energy

Outlook 2017

U.S. Energy Information

Administration

Hourly electricity generation and consumption in renewable rich areas

Centralschweizerische

Kraftwerke AG0

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250

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23

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Po

wer

[kW

]

PV surplus

Load

PV feed-in

Power to gas

Gas to power

So far, electricity and gas networks are operated

as independent systems

In the last 10 years, large areas of fluctuating

renewables resulted in excess production or

excess residual load

Therefore, electricity and gas networks are

coupled!

||


04.04.2019 3

Gas Supply Impacts Electric Power Production

Source: Report on Outages and Curtailments During the Southwest

Cold Weather Event of February 1-5, 2011 (FERC/NERC)

Giovanni Sansavini

Natural gas prices and wholesale

electricity prices are closely linked

Natural gas supply causes reliability

problems in the power generation

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04.04.2019 4

Research Question

How Can We Enable Safe Operations of Coupled Gas & Electricity Networks ?

Background

Gas constraints usually not accounted for in reserve allocation models

Previous research1 highlighted the impact of gas constraints on reserves

Research gap: need of integrated study on reserve allocation that

combines gas constraints, uncertainties and sensitivity to RES availability

1 Clegg, S. & Mancarella, P., IEEE Transactions Sustainable Energy, 2016Giovanni Sansavini

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04.04.2019 5

Gas analysis

Steady-state

Simulation

- Newton-nodal method

- Newton-loop method

-…

Optimization

- Dynamic programming methods

- Gradient search methods

- Linearization methods

- MINLP

-…

Transient

Simulation

- Method of characteristics

- Implicit and explicit finite difference and finite element methods

-…

Optimization

- Hierarchical control methods

- Mathematical programming:

-NLP

-QP

-MINLP

-…

Modelling Approaches – Gas Network

Giovanni Sansavini

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Li B., Barker K. and Sansavini G., IEEE Systems Journal, in press04.04.2019Giovanni Sansavini 6

Physics-based Modeling of Main Operations

0M

Sx t

R

P h wg f

x x t

PzR

1 1 1

1 1 1

2 2 2

1 1 1

1 0 0 0 0 0

1 1 0 0 0 0

0 1 1 0 0 0

0 0 1 1 0 0

0 0 0 1 1 0

0 0 0 0 1 1

0 0 0 0 0 1

n n

n n n

n n n

d e

a M f

d e

e

a M f

d e

Focus on Integrated Large-Scale Gas and Electric Power Network Transient Models

Antenucci A. and Sansavini G., Journal of Risk and Reliability, 2018

||


BUT without considering physical limitations of

gas flows

04.04.2019Giovanni Sansavini

Electric Power Network Stochastic Optimization Gas Network Model (t > t0)

Formulation of novel constraints for gas-fired

plants off-takes

Pressure violation

Electric gas

demands and

reserves

Antenucci A. and Sansavini G., IEEE Transactions on Sustainable Energy, 2018

Contribution: Integrated Power and Gas Network under Uncertainty

Minimize Operating Cost (t0)

Subject to Gas-fired plant capacity

Power reserve requirements

Renewable generation

Load demand

Electric network constraints

Faults…

𝑃𝑔𝑡 and 𝑅𝑔𝑡

B.C.

𝑃𝑔𝑡 − ∆𝑃𝑔𝑡 and 𝑅𝑔𝑡 − ∆𝑅𝑔𝑡 𝑔 ∈ ෩𝐺

Location and

magnitude of

pressure violation

Material

balance

Momentum

balance

Equation of

state

Safety Limit

Safety Limit

Pipelines: 304

Nodes: 244

Compressors: 24

Terminals & storages:18

||


Start

Master Problem Unit dispatch Reserve schedule

Slave Problems Forecast uncertainty

scenarios N-1 scenarios

Benderscuts

Constraints:

Gen. up-/ down time

Gen. ramp rate

Gen. capacity

Min Gen. setpoint

Reserve allocation

Reserve utilization

Power imports

RES availability

Network power

balance

Electric line capacity

04.04.2019 8

Model – Electric Network Operations

Electric network operations day-ahead stochastic N-1 secure

unit commitment

Uncertainty scenario (s): electric load, RES forecast profile and

faults

Stochastic SCUC

Giovanni Sansavini

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04.04.2019 9

Model – Gas Network OperationsStart




Benderscuts

Transient gas network simulation

Stochastic SCUC

Modelling choices:

Compressors: constant pressure ratio, maximum nominal power

Gas imports and storage: constant injections, 2-hour delay

corrections

Instant load fluctuations are compensated via linepack variation

Giovanni Sansavini

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04.04.2019

Model – Gas and Electric Network OperationsStart




Benderscuts


Stochastic SCUC In case of no pressure violation the algorithm

terminates

In case of pressure violation GFPP off-takes

nearby the violation are constrained

Pressure violation?

No

End

Yes

Constraints on GFPP outputs

10Giovanni Sansavini

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04.04.2019 11

Application: Gas-Constrained Power Reserves Allocation

Large renewables projections (wind 33% of installed capacity)

Renewables volatility compensated mainly by gas-fired power

plants (reserves)

Electric lines and generators are considered in the N-1 security criteria

Stochastic forecast scenarios – Input data:

Giovanni Sansavini

Pipelines: 304

Nodes: 244

Compressors: 24


Great Britain gas and electric power grids

Buses: 29

Generators: 57

Power lines: 98 An

ten

ucci A

. a

nd

Sa

nsa

vin

i G

.,

Jo

urn

al o

f R

isk a

nd

Re

liab

ility

, 2

01

8

Dem

and

Gas

Electricity

||


04.04.2019 12

Application: Impact of Gas Constraints – Windy Day

Combined-cycle gas turbines

(CCGT) from 33% to 30%

Coal (5%) and imports (1%)

contribution increase

A significant amount of wind

energy is curtailed (355 GWh

~40% available wind power)

Minimum pressure violations

in southern regions during

hour 18-24

30% of the reserves between

hours 18-23 are rescheduled

from zones 3-5 to zone 6

Giovanni Sansavini

Neglecting physical gas constraints

Planning for physical gas constraints

Wind

Wind

Antenucci A. and Sansavini G., IEEE

Transactions on Sustainable Energy, 2018

Gas

Gas

||


04.04.2019 13

Application: Impact of Gas Constraints – Non-Windy Day

Wind power contribution

from 42% to 4%

Combined-cycle gas

turbines (CCGT)

contribution from 30% to

47%

Power reserves are

allocated to pumped

hydro storage (PS)

If gas constraints are

neglected, security of

supply is compromised

Giovanni SansaviniAntenucci A. and Sansavini G., IEEE


Gas

Gas


Water


||


04.04.2019 14

Application: Impact of Gas Constraints – Non-Windy Day

Wind power contribution

from 42% to 4%

Combined-cycle gas

turbines (CCGT)

contribution from 30% to

47%

Power reserves are

allocated to pumped

hydro storage (PS)

If gas constraints are

neglected, security of

supply is compromised

Giovanni SansaviniAntenucci A. and Sansavini G., IEEE


Gas

Gas


Water


Gas

Water

||


15

Impact of Gas Constraints – Non-windy Day (2)Without gas constraintsWith gas constraints

Giovanni Sansavini 04.04.2019

||


Novel formulation of gas constraints in the energy system planning and

operations

Neglecting constraints of the gas grid operations leads to unsafe allocation

of power reserves

Gas constraints affect the type and location of generators that provide

reserves

Cost increase of the proposed safe reserve allocation is limited

Curtailments to critical locations protect against unexpected ramp-down

events

04.04.2019 16

Highlights

Giovanni Sansavini

Thank you for your attention!

Questions?

Backup Slides

||


BUT without considering physical limitations of

gas flows

04.04.2019Giovanni Sansavini

Electric Power Network Stochastic Optimization Gas Network Model (t > t0)

Formulation of novel constraints for gas-fired

plants off-takes

Pressure violation

Electric gas

demands and

reserves

Antenucci A. and Sansavini G., IEEE Transactions on Sustainable Energy, 2018

~20 min for 138 uncertainty scenarios (2 h parallelized) Total comp. time: ~ 6 h (× iteration ~ 5)

Contribution: Integrated Power and Gas Network under Uncertainty

Minimize Operating Cost (t0)

Subject to Gas-fired plant capacity

Power reserve requirements

Renewable generation

Load demand

Electric network constraints

Faults…

𝑃𝑔𝑡 and 𝑅𝑔𝑡

B.C.

𝑃𝑔𝑡 − ∆𝑃𝑔𝑡 and 𝑅𝑔𝑡 − ∆𝑅𝑔𝑡 𝑔 ∈ ෩𝐺

~ 4 h Euler cluster, 24 cores (2.5-3.7 GHz)

Location and

magnitude of

pressure violation

Material

balance

Momentum

balance

Equation of

state

Safety Limit

Safety Limit

Pipelines: 304

Nodes: 244

Compressors: 24


VariablesEquality

Constraints

Inequality

Constraints

949248 501552 1790159

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04.04.2019Giovanni Sansavini 20

Validation: Reproducing 2020 Electricity Generation and Reserves

0

5000

10000

15000

20000

2010 2015 2020 2025 2030

Op

era

tin

g R

ese

rve

R

eq

uir

em

en

ts [

MW

]

Year

Wind load factor 0%

Wind load factor 30%

Wind load factor 100%

Our Model

2

18

31

9

5

22

2

11

5.1

20.9

25

7.8

3.6

24.3

2.2

11.1

HYDRO N UCL EAR G AS OTHER COAL W I N D SOL AR I M PORT

% A

NN

UA

L G

ENER

AT

ION

Future Energy Scenario 2020 Model

Source: Operating the Electricity

Transmission Networks in 2020,

National Grid, 2011

Source: National Grid’s Gone Green

scenario 2020 for Great Britain, 2014

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04.04.2019 21

Implicit Method with Intermediate Step

Fundamental equations for pipeline flow

• Gas state equation: (1)

• Mass balance: (2)

• Momentum conservation: (3)

For strongly subcritical flow and considering natural gas, (3) becomes:

Hypothesis

One-dimensional, isothermal and single phase flow

Constant friction coefficient

0M

Sx t

R

P h dwg f

x x dt

PzR

*

2 2 2

11 0

2 sd sd sd

w h MM g b

x DSw Lw L Sw t

Giovanni Sansavini

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04.04.2019 22

Implicit Method with Intermediate Step (2)

Spatial discretization

The mass balance equation is discretized as:

ρ1 ρ2 ρn+1

M1 Mn-1 Mn

Q1 Q2 Qi Qn Qn+1

2Δxi-1

Qi-1

ρi-1 ρiρn

11 1

1 1 1 1

1

1 1 1 1

11

1 1

1 12,

1 1

ii i i

i i i i i i i i

nn n

n n n n

dM Q

dt x S x S

dM M Q i n

dt x S x S x S x S

dM Q

dt x S x S

Giovanni Sansavini

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04.04.2019 23


Spatial discretization

The momentum equation is discretized as:

where:

*1 12 2 2

ˆ 2 2ˆ 0

2i i i

i i i i i i ii i i i i i i

i i sd sd i sdi

w x h x dMM g b

D S w w S w dt

* *

1

1

1

1i

i i

i i i

i i i

zb a

h h h

1

1

1

2

1

2

i i i

i i i

i i i iP R z

21

1 1

1

ˆˆ

ˆ2

i

ii

i i

sd i i i

ni

i i i

Mw

S

w R z z

P P

R z z

ρ1 ρ2 ρn+1

M1 Mn-1 Mn

Q1 Q2 Qi Qn Qn+1

2Δxi-1

Qi-1

ρi-1 ρiρn

Giovanni Sansavini

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04.04.2019 24


Integration technique

Consider a differential equation:

Linearize:

Apply the implicit method

The parameter ϑ is empirically set to 0.473. Rearranging:

, : , :y f y u y solution u boundarycondition

y Ay Bu

11

2

y t t y tA y t t y t B u t t u t

t

1

1.9 1.9 0.9 1.92

I A t y t t I A t y t B t u t t u t

Giovanni Sansavini

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04.04.2019 25


Network Matrix Formulation

The mass balance and momentum conservation equations are written for the network as:

where:

1 1 1

1 1 1

2 2 2

1 1 1

1 0 0 0 0 0

1 1 0 0 0 0

0 1 1 0 0 0

0 0 1 1 0 0

0 0 0 1 1 0

0 0 0 0 1 1

0 0 0 0 0 1

n n

n n n

n n n

d e

a M f

d e

e

a M f

d e

1 1 1 1 1

1

1 1 1 1

1

0.9 1.9

0.9 1.9

0.9 1.9

0.9

i i i i i i

n n n n n

i i i i i i

e M q d

e M M q d

e M q d

f bM c

1 11

1 1

1

1.9

1.9

1.9

i i i ii

n nn

S xd

t

S x S xd

t

S xd

t

2

*1

2

1.9 2

ˆ1

2

ˆ1.9

i

i

ii

sd i

i i

i i

i

i i i ii i i

sd i

xb

w S t

w ta b

D

g h bc

w

Giovanni Sansavini

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04.04.2019 26


Non-pipe elements

Pressure regulator:

Storages:

Injection:

Withdrawal:

Compressor:

Power:

Tap gas1:

3600

1minC

P QW

m

out fixP P

CCW

In workt s tQ K V

1 21Witht s swork cushion

t t

Q K KV V

Giovanni Sansavini

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04.04.2019 27

Numerical Complexity

Reserve Study PtG Study - Design PtG Study – Daily operations

Element Variables Equality

Constraints

Inequality

Constraints

Power

Plants

207360 1440 789743

RES 304704 76176 152352

Import 96 - 192

Load

curtail

96048 - 192096

Network 327888 423936 655776

Total 949248 501552 1790159


Constraints

Inequality

Constraints

Power

Plants

74880 18720 100841

RES 14352 7176 14352

Import 1248 - 2496

Load

curtail

9048 - 18096

Network 30888 39936 61777

PtG 725 - 18120

Line

Reinf.

99 - -

Total 131420 65832 215682


Constraints

Inequality

Constraints

Power

Plants

5760 1440 7757

RES 1140 552 1104

Import 96 - 192

Load

curtail

696 - 1392

Network 2376 696 4753

Total 10068 5064 15198

Giovanni Sansavini

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04.04.2019 28

Computational Detail

Cascading Failure model (24 h) : ~ [3, 10] min

Start

Design and planning PtG locations and capacities

Line reinforcements

Electric operation optimization


Pressure violation?

No

End

CO2 balance computation

Start




Benderscuts


~ [30, 130] min

~90 min

~20 min · 365 d

~ 4 h

~ [1, 2] min · 138

scenarios

Euler cluster, 24 core (2.5-3.7 GHz)

Total: ~ 5 h (x iteration) Total: ~ 9 h (x iteration)

Giovanni Sansavini

||


Pros and Cons (in general)

+ Low computational time

+ Versatile in component representation

- Purely descriptive

- No optimality

04.04.2019 29

Transient simulation model

Implicit finite difference method with intermediate step

Introduced by J. Kràlik et all1 in 1988

+ Standard in industrial and academic analysis

+ Optimized for large and complex network problem

+ Allows freedom in component modelling

+ Provide indications of the influence of model parameters on results, correctness of behavior

and method stability, and spatial and temporal optimal discretization

1: Kràlik J, Stiegler P, Vostry Z, et al. Dynamic modeling of large-scale networks with application to gas distribution. New York, NY: Elsevier, 1988.

Giovanni Sansavini

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04.04.2019 30

Implicit finite difference method with intermediate step (3)

Efficient network solution strategy

Equations are further manipulated by applying the following decomposition method.

The solution strategy is:

1. Densities are found at crossings by solving the continuity equation. The obtained matrix is sparse.

2. Densities and mass flows are found in all internal branches, by using the densities at crossings as

boundary conditions.

3. For boundary branches, boundary conditions are represented by one density at only one crossing.

For non-pipe elements, the momentum conservation equation is replaced with the characteristic

equation of the specific non-pipe element.Giovanni Sansavini

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04.04.2019 31

Cascading Failure Model - EventsE

lectr

icity

Ga

s

𝑇0

Next hour

𝑇0 + 1

Line failure

Gas network

issue

Power

balance

𝑇3𝑇2𝑇1

Time

Time

Giovanni Sansavini

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04.04.2019 32

Line Temperature Calculation

𝑑𝑇𝑎𝑣𝑔

𝑑𝑡=

1

𝑚 ∙ 𝐶𝑝𝑅 𝑇𝑎𝑣𝑔 ∙ 𝐼2 + 𝑞𝑠 − 𝑞𝑐 − 𝑞𝑟

𝑇𝑎𝑣𝑔: average temperature of conductor

𝑚 ∙ 𝐶𝑝: 𝑡𝑜𝑡𝑎𝑙 ℎ𝑒𝑎𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟

𝑅 𝑇𝑎𝑣𝑔 : 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑎𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇𝑎𝑣𝑔

𝐼: 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑐𝑢𝑟𝑟𝑒𝑛𝑡

𝑞𝑠: ℎ𝑒𝑎𝑡 𝑔𝑎𝑖𝑛 𝑟𝑎𝑡𝑒 𝑓𝑟𝑜𝑚 𝑠𝑜𝑙𝑎𝑟 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛

𝑞𝑐: 𝑐𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛 ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠

𝑞𝑟: 𝑟𝑎𝑑𝑖𝑎𝑡𝑒𝑑 ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠

IEEE Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors. IEEE Std 738-2012 (Revision of IEEE Std 738-2006 - Incorporates IEEE Std 738-2012 Cor 1-2013), 1

(Dec. 2013).Giovanni Sansavini

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04.04.2019 33

Frequency Deviation

𝑓. 𝑑. =Δ𝑃

σΩ𝐷𝐷𝑑 +σΩ𝐺

1𝑅𝑔

Δ𝑃: 𝑝𝑜𝑤𝑒𝑟 𝑖𝑚𝑏𝑎𝑙𝑎𝑛𝑐𝑒

Ω𝐷: 𝑠𝑒𝑡 𝑜𝑓 𝑙𝑜𝑎𝑑 𝑑𝑒𝑚𝑎𝑛𝑑𝑠

Ω𝐺 : 𝑠𝑒𝑡 𝑜𝑓 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟𝑠

𝐷𝑑: 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑡ℎ 𝑙𝑜𝑎𝑑

𝑅𝑔: 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑜𝑓 𝑡ℎ𝑒 𝑔𝑡ℎ 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟

Mousavi, O. A., Bozorg, M., Cherkaoui, R. & Paolone, M. Inter-area frequency control reserve assessment regarding dynamics of cascading outages and blackouts. Electric Power Systems Research

107, 144 (Feb. 2014).

Giovanni Sansavini

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04.04.2019 34

Generators Costs and Characteristics: Reserve Study

Unit type Variable costs

(£/MWh) 1,2,3,4

Additional Reserve

costs

(£/MWh) 5

Start-up costs

(£/MW-cap) 4

MSG (%) 3,4 Min. up-time (h) 6 Min. down-time (h) 6 Ramp rates

(p.u./min) 7

Hydro 0 (must run) Not allowed 0 0 1 1 10

Pumped storage 70 +2 0 0 1 1 6

Nuclear 0 (must run) Not allowed 71 50 12 8 0.005

OCGT 67.8 +4 21 10 1 1 0.05

CCGT 53.2 +6 33 50 8 4 0.1

Coal+ CCS 52.1 +10 42 50 8 8 0.04

Other 70 +10 58.5 50 8 6 0.04

CHP 0 (must run) Not allowed 33 50 8 4 0.1

1Qadrdan, M., Abeysekera, M., Chaudry, M., Wu, J. & Jenkins, N. Role of power-to-gas in an integrated gas and electricity system in Great Britain. International Journal of Hydrogen Energy 40, 5763 (May 2015).2 Chaudry, M., Jenkins, N. & Strbac, G. Multi-time period combined gas and electricity network optimisation. Electric Power System Research 78, 1265 (July 2008).3 Clegg, S. & Mancarella, P. Integrated Electrical and Gas Network Flexibility Assessment in Low-Carbon Multi-Energy Systems. IEEE Transanctions Sustaintainable Energy 7, 718 (Dec. 2016).4 Schröder, Andreas, et al. Current and prospective costs of electricity generation until 2050. No. 68. Data Documentation, DIW, 2013.5 Hummon, M. R., et al. Fundamental drivers of the cost and price of operating reserves. No. NREL/TP-6A20-58491. National Renewable Energy Lab.(NREL), Golden, CO (United States), 2013.6 Geiger, Ansgar. Strategic Power Plant Investment Planning under Fuel and Carbon Price Uncertainty. KIT Scientific Publishing, 2011.7 European Commission. DG for Energy (ENER/B2). Study on Synergies between Electricity and Gas Balancing Markets (EGEBS) (2012).

Giovanni Sansavini

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04.04.2019 35

Generators Costs and Characteristics: PtG Study

Unit type Fuel + O&M +

CCS(£/MWh) 1,2

CO2 Emission

(gC02/MJ) 3

Start-up costs

(£/MW-cap) 4

MSG (%) 4 Min. up-time (h) 5 Min. down-time (h) 5 Ramp rates

(p.u./min) 4,6

Hydro 0+6+0 0 0 0 1 1 10

Pumped storage 0+70+0 0 0 0 1 1 6

Nuclear 5+5+0 0 71 50 12 8 0.075

OCGT+CCS 87+3+13 56.1 21 40 1 1 0.2

CCGT+CCS 50.75+3.5+8 56.1 33 40 8 4 0.1

Coal + CCS 24.3+4+17 94.6 42 50 8 8 0.06

Other + CCS 41+11+17 109.6 58.5 50 8 6 0.06

CHP + CCS 63+5+8 - 31 (heat

revenues)

56.1 33 40 8 4 0.1

1Department for Business, Energy & Industrial Strategy. Electricity Generation Costs. Crown Publishing (UK), 20162 Chaudry, M., Jenkins, N. & Strbac, G. Multi-time period combined gas and electricity network optimisation. Electric Power System Research 78, 1265 (July 2008).3 Intergovernmental Panel on Climate Change (IPCC)4 Schröder, Andreas, et al. Current and prospective costs of electricity generation until 2050. No. 68. Data Documentation, DIW, 2013.6 Geiger, Ansgar. Strategic Power Plant Investment Planning under Fuel and Carbon Price Uncertainty. KIT Scientific Publishing, 2011.6 European Commission. DG for Energy (ENER/B2). Study on Synergies between Electricity and Gas Balancing Markets (EGEBS) (2012).

Giovanni Sansavini

reliability and risk engineering

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