1. No category

EXAMENSARBETE I ELEKTROTEKNIK 300 HP, AVANCERAD NIVÅ
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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𝑃𝑛𝑅+
𝑃𝑛𝑅−
𝑠𝑒𝑐,𝑏𝑖𝑑
𝐼𝑛,𝑖
𝑠𝑒𝑐,𝐸
𝐼𝑛,𝑖
𝑡𝑒𝑟+,𝑏𝑖𝑑
𝐼𝑛,𝑖
𝑡𝑒𝑟+,𝐸
𝐼𝑢𝑛𝑖𝑡
𝑛
∝+
𝑖
∝−
𝑖
𝜆𝑠𝑒𝑐+
𝑖
¤/MWh
𝜆𝑠𝑒𝑐−
𝑖
¤/MWh
𝜆𝑡𝑒𝑟+,𝐸
𝑘,𝑏𝑖𝑑
¤
𝜆𝑡𝑒𝑟−,𝐸
𝑘,𝑏𝑖𝑑
¤
𝑈𝑛
𝜀𝑛𝑐𝑜𝑛𝑡𝑟𝑜𝑙
𝜇
+
𝐸𝑛,𝑡𝑒𝑟
+
𝐸𝑛,𝑡𝑒𝑟
-
𝑠𝑒𝑐,𝑏𝑖𝑑
𝐼𝑡𝑜𝑡𝑎𝑙
=
∑
∑
𝑠𝑒𝑐,𝑏𝑖𝑑
𝐼𝑛,𝑖
𝑛=𝑢𝑛𝑖𝑡𝑠 𝑖𝑛 𝑖=𝑝𝑜𝑤𝑒𝑟
𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑜𝑓𝑓𝑒𝑟
𝑝𝑒𝑟𝑖𝑜𝑑
𝑜𝑓𝑓𝑒𝑟𝑒𝑑
𝑠𝑒𝑐,𝑏𝑖𝑑
𝐼𝑛,𝑖
= { max (𝜆𝑠𝑒𝑐,𝑏𝑖𝑑 × 𝑃𝑛
(𝜆𝑠𝑒𝑐,𝑏𝑖𝑑 )) | 𝜆𝑠𝑒𝑐,𝑏𝑖𝑑 < 𝜆𝑐𝑙𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑒𝑐 }
𝐼 𝑠𝑒𝑐,𝑏𝑖𝑑
𝜆𝑏𝑖𝑑
𝑡𝑒𝑟+,𝑏𝑖𝑑
𝐼𝑛,𝑡𝑜𝑡𝑎𝑙
=
𝑡𝑒𝑟+,𝑏𝑖𝑑
∑ 𝐼𝑛,𝑖
𝑖=𝑜𝑓𝑓𝑒𝑟
𝑝𝑒𝑟𝑖𝑜𝑑
𝑠𝑒𝑐𝐸
𝐼𝑡𝑜𝑡𝑎𝑙
=
∑
∑
𝑠𝑒𝑐.𝐸
𝐼𝑛,𝑖
𝑛=𝑢𝑛𝑖𝑡𝑠 𝑖𝑛 𝑖=𝑝𝑜𝑤𝑒𝑟
𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜
𝑜𝑓𝑓𝑒𝑟𝑠
𝑝𝑟𝑒𝑞𝑢𝑎𝑙. 𝑖𝑛
𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
𝑠𝑒𝑐,𝐸
𝑠𝑒𝑐+
𝑠𝑒𝑐−
)
𝐼𝑛,𝑖
= (1 − 𝜇 ∗ (𝑈𝑛 + 𝜀𝑛𝑐𝑜𝑛𝑡𝑟𝑜𝑙 ))(𝑃𝑛𝑅+ ∗∝+
+ 𝑃𝑛𝑅− ∗∝−
𝑖 ∗ 𝜆𝑖
𝑖 ∗ 𝜆𝑖
∝+
𝑖
∝−
𝑖
𝜆+𝑠𝑒𝑐,𝑖
𝑈𝑛
𝜀𝑛𝑐𝑜𝑛𝑡𝑟𝑜𝑙
𝜆−𝑠𝑒𝑐,𝑖
𝑡𝑒𝑟
𝐼𝑡𝑜𝑡𝑎𝑙
=
∑
𝑡𝑒𝑟+,𝐸
𝐼𝑛,𝑘
∑
𝑢=𝑢𝑛𝑖𝑡𝑠 𝑖𝑛 𝑘=𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓𝑓𝑒𝑟𝑠
𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑝𝑟𝑒𝑞𝑢𝑎𝑙𝑖𝑓𝑖𝑒𝑑 𝑖𝑛
𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
𝑅+
𝑡𝑒𝑟+,𝐸
𝑡𝑒𝑟+,𝐸
𝑐𝑜𝑛𝑡𝑟𝑜𝑙 ))
𝐼𝑛,𝑘
= ∑(𝑓𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦+ (𝜆𝑡𝑒𝑟+,𝐸
𝑘,𝑏𝑖𝑑 ) ∗ 𝜆𝑘,𝑏𝑖𝑑 ) ∗ 𝑃𝑛 ∗ 𝑇 ∗ (1 − 𝜇 ∗ (𝑈𝑛 + 𝜀𝑛
𝑏𝑖𝑑
𝜆𝑡𝑒𝑟+,𝐸
𝑘,𝑏𝑖𝑑
𝜇
𝑝𝑎𝑟𝑡𝑖𝑎𝑙
𝑓𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦 (𝜆𝑡𝑒𝑟+,𝐸
𝑘,𝑏𝑖𝑑 )
𝑓𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦
𝑓𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦+ (𝜆𝑡𝑒𝑟+,𝐸
𝑘,𝑏𝑖𝑑 )
+
−
+
−
+
−
+
−
𝐶𝑢𝑛𝑖𝑡 𝑛 (𝐸𝑡𝑒𝑟
, 𝐸𝑡𝑒𝑟
, 𝐸𝑠𝑒𝑐
, 𝐸𝑠𝑒𝑐
) = 𝑀𝐶(𝐸𝑡𝑒𝑟
, 𝐸𝑡𝑒𝑟
, 𝐸𝑠𝑒𝑐
, 𝐸𝑠𝑒𝑐
) + 𝐹𝐶
+
𝐸𝑛,𝑠𝑒𝑐
+
𝐸𝑛,𝑡𝑒𝑟
−
𝐸𝑛,𝑠𝑒𝑐
−
𝐸𝑛,𝑡𝑒𝑟
+
𝐸𝑛,𝑡𝑒𝑟
=
∑
∑
𝑘=𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒
𝑡𝑒𝑟𝑡𝑖𝑎𝑟𝑦 𝑒𝑛𝑒𝑟𝑔𝑦
𝑜𝑓𝑓𝑒𝑟𝑠
𝑝𝑟𝑒𝑞𝑢𝑎𝑙𝑖𝑓𝑖𝑒𝑑 𝑖𝑛
𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
𝑝𝑎𝑟𝑡𝑖𝑎𝑙
+
+
𝑓𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦 (𝜆𝑡𝑒𝑟
𝑘,𝑏𝑖𝑑 ) ∗ 𝑇 ∗ 𝑃𝑛
𝑏𝑖𝑑=𝑏𝑖𝑑
𝑚𝑢𝑙𝑡𝑖−𝑙𝑒𝑣𝑒𝑙 𝑏𝑖𝑑𝑠
𝑝𝑎𝑟𝑡𝑖𝑎𝑙
−
−
𝐸𝑛,𝑡𝑒𝑟
= ∑ ∑ 𝑓𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦 (𝜆𝑡𝑒𝑟−
𝑘,𝑏𝑖𝑑 ) ∗ 𝑇 ∗ 𝑃𝑛
𝑘
𝑏𝑖𝑑
+
+
−
−
𝐸± = 𝐸𝑡𝑒𝑟
+ 𝐸𝑠𝑒𝑐
+ 𝐸𝑠𝑒𝑐
+ 𝐸𝑡𝑒𝑟
+
+
𝐸𝑡𝑒𝑟
, 𝐸𝑠𝑒𝑐
>0
−
−
𝐸𝑠𝑒𝑐
, 𝐸𝑡𝑒𝑟
<0
+
𝐸𝑡𝑒𝑟
= +1 𝑀𝑊ℎ.
−
𝐸𝑡𝑒𝑟
= − 1 𝑀𝑊ℎ.
𝐹𝐶 = 𝐶𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + ∆𝐶𝑚𝑎𝑖𝑛𝑡𝑎𝑛𝑐𝑒
+
−
+
−
𝑀𝐶(𝐸𝑡𝑒𝑟
, 𝐸𝑡𝑒𝑟
, 𝐸𝑠𝑒𝑐
, 𝐸𝑠𝑒𝑐
)
+
= ∆𝑃𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟 (𝐸± ) − ∆𝑆𝑒𝑙𝑒𝑐,𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟 (𝐸± ) + ∆𝐶𝑓𝑢𝑒𝑙 (𝐸± )) + 𝐶𝑠𝑡𝑎𝑟𝑡−𝑢𝑝 (𝐸𝑡𝑒𝑟
)
∆𝑃𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟 = 𝜃𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟 × (−𝐸 𝑎𝑐𝑡𝑢𝑎𝑙
+ 𝐸 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒 )
= 𝜃𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟 × (−𝐸± )
𝜃𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟
∆𝑃𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟
𝐸± < 0)
𝐸± > 0
∆𝑆𝑒𝑙𝑒𝑐,𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟 (𝐸± )
= 𝜃𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟 × (𝐸 𝑎𝑐𝑡𝑢𝑎𝑙
− 𝐸 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒 )
∆𝑃𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟 < 0
𝜃𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟
∆𝑆𝑒𝑙𝑒𝑐,𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟
= 𝜃𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟 × (𝐸± )
𝐸± < 0)
∆𝐶𝑓𝑢𝑒𝑙 (𝐸± ) = 𝜃𝑓𝑢𝑒𝑙 × 𝐸±
+
𝐸𝑡𝑒𝑟
1
×
) × 𝑐𝑠𝑡𝑎𝑟𝑡−𝑢𝑝
𝑃 + 1.5
𝑡𝑜𝑡𝑎𝑙 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦
= 𝑎𝑏𝑠 (
)
1.5
× 𝑐𝑠𝑡𝑎𝑟𝑡−𝑢𝑝
≈ 𝑛𝑏 𝑜𝑓 𝑠𝑡𝑎𝑟𝑡𝑢𝑝 × 𝑐𝑠𝑡𝑎𝑟𝑡−𝑢𝑝
−∆𝑆𝑒𝑙𝑒𝑐,𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟 > 0
𝜃𝑓𝑢𝑒𝑙
+ )
𝐶𝑠𝑡𝑎𝑟𝑡−𝑢𝑝 (𝐸𝑡𝑒𝑟
= 𝑎𝑏𝑠 (
𝑐𝑠𝑡𝑎𝑟𝑡−𝑢𝑝
+
𝐸𝑡𝑒𝑟
𝑀𝐶𝐺1 = ∆𝐶𝑓𝑢𝑒𝑙 + ∆𝑃𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟
+
+ 𝐶𝑠𝑡𝑎𝑟𝑡−𝑢𝑝 (𝐸𝑡𝑒𝑟
)
∆𝑃𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟
𝑀𝐶𝐺2 = ∆𝐶𝑓𝑢𝑒𝑙 − ∆𝑆𝑒𝑙𝑒𝑐,𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑟
𝑀𝐶𝐿1 = 0
∆𝑃𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟 = 0
𝑀𝐶𝐿2 = ∆𝑃𝑒𝑙𝑒𝑐,𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟
-
-
μ = 10
Portfolio: List of participating units
Simulation Market Data
Forecast method
Bidding processes
Bid acceptance processes
𝑡𝑒𝑟+,𝑏𝑖𝑑
𝐼𝑛,𝑡𝑜𝑡𝑎𝑙
=
∑
𝑡𝑒𝑟+,𝑏𝑖𝑑
𝐼𝑛,𝑖
= ∑ (𝑖𝑛𝑐𝑜𝑚𝑒𝑤𝑒𝑒𝑘𝑙𝑦 𝑏𝑖𝑑𝑠 + ∑ 𝑖𝑛𝑐𝑜𝑚𝑒𝑑𝑎𝑖𝑙𝑦 𝑏𝑖𝑑𝑠 )
𝑖=𝑜𝑓𝑓𝑒𝑟
𝑝𝑒𝑟𝑖𝑜𝑑
𝑤𝑒𝑒𝑘𝑠
𝑏𝑙𝑜𝑐𝑘𝑠
Delivery calls models
∝+
𝑖
∝−
𝑖
𝜆𝑠𝑒𝑐+
𝑖
𝜆𝑠𝑒𝑐−
𝑖
∝+
𝑖
∝−
𝑖
𝑓𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦
𝜆𝐸𝑛𝑒𝑟𝑔𝑦
𝜆𝐸𝑛𝑒𝑟𝑔𝑦 (𝑓) = 𝐴 ∗ 𝑒 −𝑓∗𝑋 ⇔
𝑓𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦 (𝜆𝐸𝑛𝑒𝑟𝑔𝑦 ) = −
1
𝜆
∗ ln ( )
𝑋
𝐴
≈ 40 €/𝑀𝑊ℎ
Market revenue from the delivery of control energy
≈ 40 €/𝑀𝑊ℎ
-
-
𝑓𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦
𝜆𝐸𝑛𝑒𝑟𝑔𝑦
𝑓𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦 (𝜆𝐸𝑛𝑒𝑟𝑔𝑦 ) = −
1
𝜆
∗ ln ( )
𝑋
𝐴
-
-
≤
=
≤
≤
>
>
-
-
-
.
Bidding Strategy
XX
X
XX
XX
XX
XX
X
X
X
X
X
X
XX
X
X
XX
XX
X
XX
X
XXX
XX
XX
XX
X
XX
XX
X
X
X
XX
Bidding Strategy
XX
XXX
X
XXX
X
XX
X
X
XXX
XX
XX
XX
X
XX
XX
X
XX
XX
X
X
X
X
X
XX
X
X
X
X
XX
X
X
X
X
X
X
X
Bidding Strategy
X
X
X
X
XX
XX
X
XX
X
-
𝑝
𝑥𝑡 = 𝑐 + ∑ 𝜙𝑖 𝑥𝑡−𝑖
𝑖=1
𝜙𝑖
𝑝
𝑥𝑡 = 𝑐 + ∑ 𝜙𝑠.𝑖 𝑥𝑡−𝑠.𝑖
𝑖=1
𝜙𝑖
𝐴𝑅(3) + 𝑆𝐴𝑅52 (1) ∶ 𝑥̂𝑡 = 𝜙1 𝑥𝑡−1 + 𝜙2 𝑥𝑡−2 + 𝜙3 𝑥𝑡−3 + 𝜙52 𝑥𝑡−52
𝐴𝑅(1) + 𝑆𝐴𝑅6 (2) ∶ 𝑥̂𝑡 = 𝜙1 𝑥𝑡−1 + 𝜙6 𝑥𝑡−6 + 𝜙12 𝑥𝑡−12
MWh/MW/week
25
20
αi + (MWh/MW/week)
αi - (MWh/MW/week)
15
10
5
0
-5
-10
-15
-20
-25
Week
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