An Economical & TechnicalStudy of the Participation of aVirtual Power Plant on the SwissBalancing Market

I , AVANCERAD NIVÅ EXAMENSARBETE ELEKTROTEKNIK 300 HP

STOCKHOLM SVERIGE 2016 ,

An Economical & Technical Study of the Participation of a Virtual Power Plant on the Swiss Balancing Market

WRITTEN IN COLLABORATION WITH SWISSELECTRICITY

ROMAIN BOURDETTE

KTH KUNGLIGA TEKNISKA HÖGSKOLAN

SKOLAN FÖR ELEKTRO- OCH SYSTEMTEKNIK

TRITA EE 2016:018

www.kth.se

BACKGROUND STUDY

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-

¤

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¤

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¤

¤

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¤

¤

¤

𝑃

𝑛𝑅+

𝑃

_𝑛^𝑅−

𝐼

_𝑛,𝑖^{𝑠𝑒𝑐,𝑏𝑖𝑑}

𝐼

_𝑛,𝑖^{𝑠𝑒𝑐,𝐸}

𝐼

_𝑛,𝑖^{𝑡𝑒𝑟+,𝑏𝑖𝑑}

𝐼

_{𝑢𝑛𝑖𝑡 𝑛}^{𝑡𝑒𝑟+,𝐸}

∝

_𝑖⁺

∝

𝑖−

𝜆

_𝑖^{𝑠𝑒𝑐+}

¤/MWh

𝜆

_𝑖^{𝑠𝑒𝑐−}

¤/MWh

𝜆

_{𝑘,𝑏𝑖𝑑}^{𝑡𝑒𝑟+,𝐸}

¤

𝜆

_{𝑘,𝑏𝑖𝑑}^{𝑡𝑒𝑟−,𝐸}

¤

𝑈

𝑛

𝜀

𝑛𝑐𝑜𝑛𝑡𝑟𝑜𝑙

𝜇

𝐸

_{𝑛,𝑡𝑒𝑟}⁺

𝐸

_{𝑛,𝑡𝑒𝑟}⁺

-

-

𝐼

_{𝑡𝑜𝑡𝑎𝑙}^{𝑠𝑒𝑐,𝑏𝑖𝑑}

= ∑ ∑ 𝐼

_𝑛,𝑖^{𝑠𝑒𝑐,𝑏𝑖𝑑}

𝑖=𝑝𝑜𝑤𝑒𝑟 𝑜𝑓𝑓𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑛=𝑢𝑛𝑖𝑡𝑠 𝑖𝑛

𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜

𝐼

_𝑛,𝑖^{𝑠𝑒𝑐,𝑏𝑖𝑑}

= { max (𝜆

^{𝑠𝑒𝑐,𝑏𝑖𝑑}

× 𝑃

_𝑛^{𝑜𝑓𝑓𝑒𝑟𝑒𝑑}

(𝜆

^{𝑠𝑒𝑐,𝑏𝑖𝑑}

)) | 𝜆

^{𝑠𝑒𝑐,𝑏𝑖𝑑}

< 𝜆

𝑐𝑙𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑒𝑐

}

𝐼

^{𝑠𝑒𝑐,𝑏𝑖𝑑}

𝜆

^𝑏𝑖𝑑

𝐼

_{𝑛,𝑡𝑜𝑡𝑎𝑙}^{𝑡𝑒𝑟+,𝑏𝑖𝑑}

= ∑ 𝐼

_𝑛,𝑖^{𝑡𝑒𝑟+,𝑏𝑖𝑑}

𝑖=𝑜𝑓𝑓𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑

𝐼

𝑡𝑜𝑡𝑎𝑙𝑠𝑒𝑐𝐸

= ∑ ∑ 𝐼

𝑛,𝑖𝑠𝑒𝑐.𝐸

𝑖=𝑝𝑜𝑤𝑒𝑟

𝑜𝑓𝑓𝑒𝑟𝑠 𝑝𝑟𝑒𝑞𝑢𝑎𝑙. 𝑖𝑛

𝑝𝑒𝑟 𝑦𝑒𝑎𝑟

𝑛=𝑢𝑛𝑖𝑡𝑠 𝑖𝑛

𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜

𝐼

_𝑛,𝑖^{𝑠𝑒𝑐,𝐸}

= (1 − 𝜇 ∗ (𝑈

𝑛

+ 𝜀

𝑛𝑐𝑜𝑛𝑡𝑟𝑜𝑙

))(𝑃

_𝑛^𝑅+

∗∝

⁺_𝑖

∗ 𝜆

_𝑖^{𝑠𝑒𝑐+}

+ 𝑃

𝑛𝑅−

∗∝

_𝑖⁻

∗ 𝜆

_𝑖^{𝑠𝑒𝑐−}

)

∝

_𝑖⁺

∝

_𝑖⁻

𝜆

_{𝑠𝑒𝑐,𝑖}⁺

𝜆

_{𝑠𝑒𝑐,𝑖}⁻

𝑈 _𝑛

𝜀 _𝑛 ^{𝑐𝑜𝑛𝑡𝑟𝑜𝑙}

𝐼

_{𝑡𝑜𝑡𝑎𝑙}^𝑡𝑒𝑟

= ∑ ∑ 𝐼

_𝑛,𝑘^{𝑡𝑒𝑟+,𝐸}

𝑘=𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓𝑓𝑒𝑟𝑠 𝑝𝑟𝑒𝑞𝑢𝑎𝑙𝑖𝑓𝑖𝑒𝑑 𝑖𝑛

𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 𝑢=𝑢𝑛𝑖𝑡𝑠 𝑖𝑛

𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜

𝐼

_𝑛,𝑘^{𝑡𝑒𝑟+,𝐸}

= ∑(𝑓

_{𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦+}

(𝜆

^{𝑡𝑒𝑟+,𝐸}_{𝑘,𝑏𝑖𝑑}

)

𝑏𝑖𝑑

∗ 𝜆

_{𝑘,𝑏𝑖𝑑}^{𝑡𝑒𝑟+,𝐸}

) ∗ 𝑃 _𝑛 ^𝑅+ ∗ 𝑇 ∗ (1 − 𝜇 ∗ (𝑈

_𝑛

+ 𝜀

_𝑛^{𝑐𝑜𝑛𝑡𝑟𝑜𝑙}

))

𝜆

^{𝑡𝑒𝑟+,𝐸}_{𝑘,𝑏𝑖𝑑}

𝜇

𝑓

_{𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦}^{𝑝𝑎𝑟𝑡𝑖𝑎𝑙}

(𝜆

^{𝑡𝑒𝑟+,𝐸}_{𝑘,𝑏𝑖𝑑}

) 𝑓

𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦

𝑓

_{𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦+}

(𝜆

^{𝑡𝑒𝑟+,𝐸}_{𝑘,𝑏𝑖𝑑}

)

𝐶

𝑢𝑛𝑖𝑡 𝑛

(𝐸

𝑡𝑒𝑟+

, 𝐸

𝑡𝑒𝑟−

, 𝐸

𝑠𝑒𝑐+

, 𝐸

𝑠𝑒𝑐−

) = 𝑀𝐶(𝐸

𝑡𝑒𝑟+

, 𝐸

𝑡𝑒𝑟−

, 𝐸

𝑠𝑒𝑐+

, 𝐸

𝑠𝑒𝑐−

) + 𝐹𝐶

𝐸

𝑛,𝑠𝑒𝑐+

𝐸

𝑛,𝑠𝑒𝑐−

𝐸

_{𝑛,𝑡𝑒𝑟}⁺

𝐸

_{𝑛,𝑡𝑒𝑟}⁻

𝐸

𝑛,𝑡𝑒𝑟+

= ∑ ∑ 𝑓

_{𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦}^{𝑝𝑎𝑟𝑡𝑖𝑎𝑙}

(𝜆

^{𝑡𝑒𝑟 +}_{𝑘,𝑏𝑖𝑑}

)

𝑏𝑖𝑑=𝑏𝑖𝑑 𝑚𝑢𝑙𝑡𝑖−𝑙𝑒𝑣𝑒𝑙 𝑏𝑖𝑑𝑠

∗ 𝑇

𝑘=𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑡𝑒𝑟𝑡𝑖𝑎𝑟𝑦 𝑒𝑛𝑒𝑟𝑔𝑦

𝑜𝑓𝑓𝑒𝑟𝑠 𝑝𝑟𝑒𝑞𝑢𝑎𝑙𝑖𝑓𝑖𝑒𝑑 𝑖𝑛

𝑝𝑒𝑟 𝑦𝑒𝑎𝑟

∗ 𝑃

𝑛+

𝐸

𝑛,𝑡𝑒𝑟−

= ∑ ∑ 𝑓

_{𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦}^{𝑝𝑎𝑟𝑡𝑖𝑎𝑙}

(𝜆

𝑘,𝑏𝑖𝑑𝑡𝑒𝑟−

)

𝑏𝑖𝑑

∗ 𝑇 ∗ 𝑃

𝑛− 𝑘

𝐸

±

= 𝐸

𝑡𝑒𝑟+

+ 𝐸

𝑠𝑒𝑐+

+ 𝐸

𝑠𝑒𝑐−

+ 𝐸

𝑡𝑒𝑟−

𝐸

_𝑡𝑒𝑟⁺

, 𝐸

_𝑠𝑒𝑐⁺

> 0 𝐸

_𝑠𝑒𝑐⁻

, 𝐸

_𝑡𝑒𝑟⁻

< 0

𝐸

_𝑡𝑒𝑟⁺

= +1 𝑀𝑊ℎ.

𝐸

𝑡𝑒𝑟−

= − 1 𝑀𝑊ℎ.

𝐹𝐶 = 𝐶

𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

+ ∆𝐶

𝑚𝑎𝑖𝑛𝑡𝑎𝑛𝑐𝑒

𝑀𝐶(𝐸

𝑡𝑒𝑟+

, 𝐸

𝑡𝑒𝑟−

, 𝐸

𝑠𝑒𝑐+

, 𝐸

𝑠𝑒𝑐−

)

= ∆𝑃

𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟

(𝐸

_±

) − ∆𝑆

𝑒𝑙𝑒𝑐,𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟

(𝐸

_±

) + ∆𝐶

_{𝑓𝑢𝑒𝑙}

(𝐸

_±

)) + 𝐶

_{𝑠𝑡𝑎𝑟𝑡−𝑢𝑝}

(𝐸

_𝑡𝑒𝑟⁺

)

∆𝑃

𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟

= 𝜃

𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟

× (−𝐸

^{𝑎𝑐𝑡𝑢𝑎𝑙}

+ 𝐸

^{𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒}

)

= 𝜃

𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟

× (−𝐸

±

)

𝜃

_{𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟}

∆𝑃

𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟

𝐸

±

< 0)

𝐸

±

> 0 ∆𝑃

𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟

< 0

∆𝑆

𝑒𝑙𝑒𝑐,𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟

(𝐸

±

)

= 𝜃

𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟

× (𝐸

^{𝑎𝑐𝑡𝑢𝑎𝑙}

− 𝐸

^{𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒}

)

= 𝜃

𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟

× (𝐸

±

)

𝜃

_{𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟}

∆𝑆

𝑒𝑙𝑒𝑐,𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟

𝐸

_±

< 0)

−∆𝑆

𝑒𝑙𝑒𝑐,𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟

> 0

∆𝐶

𝑓𝑢𝑒𝑙

(𝐸

±

) = 𝜃

𝑓𝑢𝑒𝑙

× 𝐸

±

𝜃

𝑓𝑢𝑒𝑙

𝐶

_{𝑠𝑡𝑎𝑟𝑡−𝑢𝑝}

(𝐸

𝑡𝑒𝑟+

) = 𝑎𝑏𝑠 ( 𝐸

_𝑡𝑒𝑟⁺

𝑃

⁺

× 1

1.5 ) × 𝑐

_{𝑠𝑡𝑎𝑟𝑡−𝑢𝑝}

= 𝑎𝑏𝑠 ( 𝑡𝑜𝑡𝑎𝑙 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦

1.5 )

× 𝑐

𝑠𝑡𝑎𝑟𝑡−𝑢𝑝

≈ 𝑛𝑏 𝑜𝑓 𝑠𝑡𝑎𝑟𝑡𝑢𝑝 × 𝑐

𝑠𝑡𝑎𝑟𝑡−𝑢𝑝

𝐸

_𝑡𝑒𝑟⁺

𝑐

_{𝑠𝑡𝑎𝑟𝑡−𝑢𝑝}

𝑀𝐶

𝐺1

= ∆𝐶

𝑓𝑢𝑒𝑙

+ ∆𝑃

𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟

+ 𝐶

𝑠𝑡𝑎𝑟𝑡−𝑢𝑝

(𝐸

𝑡𝑒𝑟+

)

∆𝑃

𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟

𝑀𝐶

_𝐺2

= ∆𝐶

_{𝑓𝑢𝑒𝑙}

− ∆𝑆

𝑒𝑙𝑒𝑐,𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟

𝑀𝐶

𝐿1

= 0

∆𝑃

𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟

= 0

𝑀𝐶

𝐿2

= ∆𝑃

𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟

-

-

-

-

μ = 10

Portfolio: List of participating units

Simulation Market Data

Forecast method

Bidding processes

Bid acceptance processes

𝐼

_{𝑛,𝑡𝑜𝑡𝑎𝑙}^{𝑡𝑒𝑟+,𝑏𝑖𝑑}

= ∑ 𝐼

_𝑛,𝑖^{𝑡𝑒𝑟+,𝑏𝑖𝑑}

𝑖=𝑜𝑓𝑓𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑

= ∑ (𝑖𝑛𝑐𝑜𝑚𝑒

𝑤𝑒𝑒𝑘𝑙𝑦 𝑏𝑖𝑑𝑠

+ ∑ 𝑖𝑛𝑐𝑜𝑚𝑒

𝑑𝑎𝑖𝑙𝑦 𝑏𝑖𝑑𝑠 𝑏𝑙𝑜𝑐𝑘𝑠

)

𝑤𝑒𝑒𝑘𝑠

Delivery calls models

∝

_𝑖⁺

∝

_𝑖⁻

𝜆

_𝑖^{𝑠𝑒𝑐+}

𝜆

_𝑖^{𝑠𝑒𝑐−}

∝

_𝑖⁺

∝

_𝑖⁻

𝑓

_{𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦}

𝜆

𝐸𝑛𝑒𝑟𝑔𝑦

𝜆

𝐸𝑛𝑒𝑟𝑔𝑦

(𝑓) = 𝐴 ∗ 𝑒

^{−𝑓∗𝑋}

⇔ 𝑓

𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦

(𝜆

𝐸𝑛𝑒𝑟𝑔𝑦

) = − 1

𝑋 ∗ ln ( 𝜆 𝐴 )

≈ 40 €/𝑀𝑊ℎ ≈ 40 €/𝑀𝑊ℎ

Market revenue from the delivery of control energy

-

-

-

-

-

𝑓

_{𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦}

𝜆

𝐸𝑛𝑒𝑟𝑔𝑦

𝑓

𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦

(𝜆

𝐸𝑛𝑒𝑟𝑔𝑦

) = − 1 𝑋 ∗ ln ( 𝜆

𝐴 )

-

-

-

-

-

-

-

≤ =

≤ ≤

> >

-

-

-

-

.

XX X

XX XX

XX XX X

X X XX X

X X XX X

X XX XXX XX

X X XX XX

XX X X

X

X

XX XX XX

Bidding Strategy

XX

XXX X

XXX X

XX X

X XX

XXX XX

XX X X

XX XX

X XX

XX X

X

X XX

X X X X X X

X

X X

X X XX X

Bidding Strategy

X X X X

XX

XX X

XX X

Bidding Strategy

-

-

𝑥

𝑡

= 𝑐 + ∑ 𝜙

𝑖

𝑥

𝑡−𝑖 𝑝

𝑖=1

𝜙

_𝑖

𝑥

𝑡

= 𝑐 + ∑ 𝜙

𝑠.𝑖

𝑥

𝑡−𝑠.𝑖 𝑝

𝑖=1

𝜙

𝑖

𝐴𝑅(3) + 𝑆𝐴𝑅

52

(1) ∶ 𝑥 ̂ = 𝜙

_𝑡 1

𝑥

𝑡−1

+ 𝜙

2

𝑥

𝑡−2

+ 𝜙

3

𝑥

𝑡−3

+ 𝜙

52

𝑥

𝑡−52

𝐴𝑅(1) + 𝑆𝐴𝑅

6

(2) ∶ 𝑥 ̂ = 𝜙

𝑡 1

𝑥

𝑡−1

+ 𝜙

6

𝑥

𝑡−6

+ 𝜙

12

𝑥

𝑡−12

-25 -20 -15 -10 -5 0 5 10 15 20 25

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 MWh/MW/week

Week αi + (MWh/MW/week)

αi - (MWh/MW/week)