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Motivation Detailed VOLL data Theory Illustration Conclusions References

How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Marten Ovaere, Evelyn Heylen, Stef Proost, Geert Deconinck, Dirk Van Hertem

KU Leuven, Department of Economics

September 6, 2017

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Motivation

◮ Value of lost load (VOLL) = cost of unserved energy. ◮ On average: VOLL = 10 e/kWh ←

→ price = 0.2 e/kWh But VOLL differs widely among consumers and over time

◮ Various empirical studies have estimated VOLL for different

countries and for different interruption characteristics.

◮ This paper analyses the efficiency gains of using more detailed

VOLL data in ex-ante decision making.

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Interruption costs

Table: Studies that estimate VOLL as a function of different interruption characteristics.

Country Consumer type Time Duration Advance notification Location Source Australia x x (CRA International, 2008) Austria x x x (Reichl et al., 2013) Cyprus x x (Zachariadis and Poullikkas, 2012) Germany x x (Growitsch et al., 2013) Great Britain x x (London Economics, 2013) Ireland x x x (Leahy and Tol, 2011) Netherlands x x x (de Nooij et al., 2007) New Zealand x x x x (Electricity Authority, 2013) Norway x x x x (EnergiNorge, 2012) Portugal x x (Castro et al., 2016) Spain x x (Linares and Rey, 2013) Sweden x x (Carlsson and Martinsson, 2008) United States x x x x x (Sullivan et al., 2009)

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Interruption costs

Table: Great Britain VOLL as a function of time characteristics and consumer groups (London Economics, 2013, Table 1 and Table 2). Expressed in [2015e/MWh].

Not winter Winter Weekday Weekend Weekday Weekend Peak Not peak Peak Not peak Peak Not peak Peak Not peak Residential 11,093 8,081 10,753 12,946 12,757 10,571 11,952 13,730 SMEs 44,077 42,849 38,749 39,722 51,284 45,551 41,224 46,306

Estimating VOLL Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Interruption costs

Table: United States VOLL as a function of time characteristics and consumer groups ((Sullivan et al., 2009, Table 3-10, Table 4-10 and Table 5-11)). Expressed in [2015e/MWh].

Summer Weekday Weekend Morning Afternoon Evening Night Morning Afternoon Evening Night Residential 2,947 2,210 2,097 2,097 3,457 2,607 2,493 2,493 Small C&I 265,004 322,100 169,713 169,319 163,019 204,364 96,866 95,291 Large C&I 15,351 21,573 18,184 13,550 11,030 15,711 12,831 9,576 Winter Weekday Weekend Morning Afternoon Evening Night Morning Afternoon Evening Night Residential 2,097 1,473 1,190 1,190 2,437 1,757 1,417 1,417 Small C&I 365,415 458,343 214,996 211,452 216,177 279,967 117,342 113,798 Large C&I 12,557 18,448 14,019 10,503 8,667 12,948 9,468 7,109

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Interruption costs

Table: Norwegian VOLL as a function of time characteristics and consumer groups (EnergiNorge, 2012, Table A and Table B).

Residential Industry Commercial Public VOLL [2015 e/MWh] 469 10,926 17,984 15,888 Season fy(c, y) Winter 1 1 1 1 Spring 0.57 0.87 1 0.67 Summer 0.44 0.86 1.02 0.51 Autumn 0.75 0.88 1.06 0.58 Day fd(c, d) Weekday 1 1 1 1 Saturday 1.07 0.13 0.45 0.3 Sunday 1.07 0.14 0.11 0.29 Time fh(c, h) 2 AM 0.4 0.12 0.11 0.43 8 AM 0.69 1 1 1 6 PM 1 0.14 0.29 0.31

V (c, t(h, d, y)) = V (c)fh(c, h)fd(c, d)fy(c, y) (1)

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Optimal reliability level

[e/MWh] ρ 1 ¯ V C ′(ρ) ¯ ρ

Figure: Efficiency gains if VOLL differs over time.

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Optimal reliability level over time

[e/MWh] ρ 1 ¯ V Vw Vs C ′(ρ) ¯ ρ ρw ρs

Figure: Efficiency gains if VOLL differs over time.

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Optimal reliability level between consumers

[e/MWh] ρ 1

¯ V

C ′(ρ) ¯ ρ

Figure: Efficiency gains if VOLL differs between consumers.

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Optimal reliability level between consumers

[e/MWh] ρ 1

Vmax Vmin ¯ V

C ′(ρ) ¯ ρ ρp Perfect Random

Figure: Efficiency gains if VOLL differs between consumers.

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Optimal reliability level between consumers

[e/MWh] ρ 1

Vmax Vmin V1 V2 ¯ V

C ′(ρ) ρs ¯ ρ ρp Perfect Spatial Random

Figure: Efficiency gains if VOLL differs between consumers.

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Optimal reliability level between consumers

[e/MWh] ρ 1

Vmax Vmin V1 V2 ¯ V

C ′(ρ) ρs ¯ ρ ρp Perfect Spatial Random

Figure: Efficiency gains if VOLL differs between consumers.

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References Data

Network: 5-node version of the RBTS

1 2 3 4 5

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References Data

Main assumptions

◮ Operational planning + real-time operation stage

More details

◮ Conventional and wind generation ◮ Dispatch, preventive redispatch and corrective redispatch costs ◮ A year = 72 time instants (6x3x4), each with its probability of

• ccurrence.

◮ Each consumer group has a different VOLL for each time

instant.

◮ Demand shares of different consumer groups change over

time.

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References Evaluation of short-term reliability management

Evaluation according to three criteria

(1) Expected total costs ETC(v) =

• t∈T

[Cprev(ap(v, t)) +

• rt∈RT

πrt

• Ccorr(art

c (v, t))

+Prt

curt(c, v, t) · V(c,t)

• ]

∀t (2) (2) Average interruption time [min/year] (3) Inequality between consumers G = |1 − (

• k

(Xk − Xk−1) · (Yk + Yk−1)| (3) = A A + B (4)

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References Evaluation of short-term reliability management

Inequality index

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 Cumulative relative demand (Dk) Cumulative relative energy not supplied (Ek) D1 D2 D3 D4 D5 E1 E2 E3 E4 E5

A B

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References Results

Results: efficiency

Table: Relative expected total system cost savings for the three countries using VOLL data with different levels of detail

∆ETC [%] V V (t) V (n, t) V (c, t) Norway

• 10.68
• 20.27
• 43.28

GB

• 0.01
• 3.03
• 9.37

US

• 0.95
• 11.14
• 29.52

∆ETC = ETC(v) − ETC(V ) ETC(V ) (5) where v ∈ {V , V (t), V (n, t), V (c, t)}.

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References Results

Results: efficiency

V vt vn vc V vt vn vc V vt vn vc 50 100 Norway GB US Relative ETC [%] Case Country

Preventive redispatch Corrective redispatch Load curtailment

Reference = V for US

Figure: Evolution of cost terms in expected total system cost for different levels of detail of VOLL

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References Results

Results: efficiency vs. equity

Norway GB US V vt vn vc V vt vn vc V vt vn vc Efficiency

• 10.68
• 20.27
• 43.28
• 0.01
• 3.03
• 9.37
• 0.95
• 11.14
• 29.52

Equity 0.66 0.58 0.81 0.75 0.7 0.7 0.82 0.74 0.68 0.64 0.85 0.73

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Conclusions

This paper:

• 1. Uses detailed VOLL data (that is already available) in ex-ante

decision making.

• 2. Shows theoretically and numerically the possible efficiency

gains of using this detailed VOLL data. Numerical illustration:

◮ Efficiency gains of 3% - 20% for spatial curtailment. ◮ Efficiency gains of 9% - 43% for perfect curtailment.

• 3. Shows that increased efficiency leads to increased inequality.
• 4. Calls for more studies to improve VOLL data. Roll-out of

smart meters facilitates this.

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Estimating VOLL

◮ Stated preference: based surveys or interviews

◮ Direct worth method ◮ Contingent valuation ◮ Preparatory action method ◮ Conjoint analysis

◮ Revealed preference: based on observed market behaviour ◮ Production function approach ◮ Case studies

Back Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Short-term reliability management

• 1. Real-time operation

Back

min

aRT

c

,PRT

curt

CRT(v) = min

aRT

c

,PRT

curt

• Ccorr(art

c ) + Prt curt(c) · v

• (6)

s.t. operational limits v ∈ {V , V (t), V (n, t), V (c, t)} = level of VOLL detail

• 2. Operational planning

min

ap,as

c,Ps curt

COP(v) = min [Cprev(ap)+

• s∈S

πs (Ccorr(as

c) + Ps curt(c) · v)

• (7)

s.t. operational limits ∀s ∈ S

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Network: line data

Table: Line data

From To x [pu] Capacity Failure node node [MW] [MVA] probab. 1 3 0.18 85 0.0017 2 4 0.6 71 0.0057 1 4 0.48 71 0.0046 3 4 0.12 71 0.0011 3 5 0.12 71 0.0011 1 3 0.18 85 0.0017 4 5 0.12 71 0.0011

Back Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Generation

Node Capacity Type Cmarg Failure [MW] [e/MWh] probab. 1 40 conv. 13.83 0.0062 1 40 conv. 13.83 0.0062 1 10 conv. 13.83 0.0062 1 20 wind 0.04 0.0062 2 40 conv. 13.83 0.0062 2 20 conv. 13.83 0.0062 2 20 wind 0.01 0.0062 2 20 wind 0.03 0.0062 2 20 wind 0.05 0.0062 2 5 conv. 13.83 0.0062 2 5 conv. 13.83 0.0062

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Generation: preventive and corrective redispatch

c+

prev = 1.5 · Cmarg + 5

c−

prev = −0.5 · Cmarg + 5

c+

corr = 5 · C + prev

c−

corr = −1

5 · C +

prev

(8)

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

Demand and VOLL

Residential Non- residential Time fH(c, h) 2 AM 0.7 1.3 8 AM 1.3 0.7 2 PM 0.8 1.2 6 PM 1.3 0.7 Day fD(c, d) Weekday 0.8 1.2 Saturday 1.15 0.85 Sunday 1.3 0.7 Season fY (c, y) Winter 1 1 Spring 0.9 1.1 Summer 1.1 0.9 Autumn 1 1

Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

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Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

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Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity

Motivation Detailed VOLL data Theory Illustration Conclusions References

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Marten Ovaere KU Leuven, Department of Economics How detailed value of lost load data impact power system reliability decisions: a trade-off between efficiency and equity