zero-carbon analytics · zero-carbon analytics andy philpott electric power optimization centre...

Zero-Carbon Analytics

Andy Philpott

Electric Power Optimization Centrewww.epoc.org.nz

University of AucklandNew Zealand

(Joint work with Michael Ferris and Anthony Downward)

Supported by Marsden grant UOA1520

INFORMS, Seattle, October 21, 2019

Philpott (www.epoc.org.nz) Zero-Carbon Analytics INFORMS October 21, 2019 1 / 55

Extinction Rebellion October 2019(http://rebellion.earth/international-rebellion.)

Wellington Extinction Rebellion protest, October 8(Photo from Getty Images)

Wellington student protest, September 27, 2019(Photo by Kevin Stent, Stuff.)

Wellington student protest, September 27, 2019(Photo by Joe Lloyd, Stuff.)

Jacinda’s 2017 election deal

Introduce a Zero Carbon Act and establish anindependent Climate Commission.Request the Climate Commission to plan the transitionto 100% renewable electricity by 2035 (which includesgeothermal) in a normal hydrological year.

Stimulate up to $1 billion of new investment in lowcarbon industries by 2020, kick-started by aGovernment-backed Green Investment fund of $100M.

(Confidence and Supply Agreement between the New Zealand LabourParty and the Green Party of Aoteoroa)

This talk is about

OR: helping government policy . . .

I to distinguish between objectives and actions;

I to understand effects of uncertainty;

I to understand effects of incentives.

This talk is about

Summary

1 Introduction

2 Understanding uncertainty

3 Getting to 100 percent renewable electricity

4 Results

5 Understanding incentives

Summary

1 Introduction

4 Results

Renewable electricity is intermittent and random

[Source: http://www.caiso.com]

Duck curve shows increasing need for ramping plant in evening.

Electricity systems also need backup capacity to ensure supplywith random renewable generation (e.g. wind).

Very large literature on these topics (see e.g. ENRE sessions)using stochastic optimization models of various sorts.

Hydro reservoirs have uncertain inflows

Ohau A power station in New Zealand’s South Island(Photo by By Ulrich Lange, Bochum, Germany - Own work)

If inflows are too low in winter then there is an energy shortage.

Need sufficient backup energy to ensure supply.

Hydro reservoirs have uncertain inflows

Ohau A power station in New Zealand’s South Island(Photo by By Ulrich Lange, Bochum, Germany - Own work)

If inflows are too low in winter then there is an energy shortage.

Need sufficient backup energy to ensure supply.

Hydroelectric reservoir optimization

Stochastic dynamic programming applied to

P: min limT→∞ E [ 1T

∑Tt=1 C (Xt ,Ut)]

s.t. Xt+1 = ft(Xt ,Ut , ωt),Ut ∈ U ,Xt ∈ X .

Popular finite-horizon approach is Stochastic Dual DynamicProgramming (SDDP) [Pereira & Pinto, 1991].

Use infinite horizon SDDP with discounting [Shapiro & Ding,2019], or average cost per year (e.g. formulation P above)[Downward & P., 2019]. We implement P in sddp.jl package[Dowson & Kapelevich, 2016].

∑Tt=1 C (Xt ,Ut)]

Optimized hydro with 500 MW coal capacity

Source: [Fulton, 2018]

CO2 emissions comparison

Summary

1 Introduction

4 Results

100 percent renewable electricity for New Zealand

New Zealand GHG emissions (80 MT CO2-e) by sector in 2017

Integrated assessment modelsClimate economy models and energy economy models [Anadon et al, 2017]

DICE [Nordhaus, 1992-2017]

MERGE [Manne et al, 1995]

MARKAL/TIMES [Loulou et al, 2008]

GCAM [Calvin et al, 2011]

[Hope, 2011]

AIM/GCE [Fujimori et al, 2012]

FUND [Anthoff & Tol, 2013]

IMAGE [Stehfest et al, 2014]

REMIND [Luderer, 2015]

WITCH [Emmerling et al, 2016]

EMPIRE [Skar et al, 2016]

MESSAGE [Huppman et al, 2019]

ReEDS [Cohen et al, 2019]

Texas Case Study [Boffino et al, 2019]

Gemstone [Ferris & P., 2019]

Simplified two-stage stochastic model

Capacity decisions are x at cost K (x).Operating decisions are: generation y at cost C (y)

loadshedding q at cost Vq.Random demand is d(ω).

Minimize annual capital cost plus expected operating cost.

P: min K (x) + Eω[C (y(ω))− V (d(ω)− q(ω))]s.t. y(ω) ≤ x ,

y(ω) + q(ω) ≥ d(ω),x , y(ω), q(ω) ≥ 0.

Simplified two-stage risk-averse model

loadshedding q at cost Vq.Random demand is d(ω), and F a coherent risk measure.

Minimize annual capital cost plus risk-adjusted operating cost.

P: min K (x) + Fω[C (y(ω))− V (d(ω)− q(ω))]s.t. y(ω) ≤ x ,

y(ω) + q(ω) ≥ d(ω),x , y(ω), q(ω) ≥ 0.

Penalize load shedding at V (value of lost load)

loadshedding q at cost Vq.Random demand is d(ω).

Minimize annual capital cost plus expected operating cost.

P: min K (x) + Eω[C (y(ω))− V (d(ω)− q(ω))]s.t. y(ω) ≤ x ,

y(ω) + q(ω) ≥ d(ω),x , y(ω), q(ω) ≥ 0.

Gemstone: New Zealand capacity expansion model

[described in full in Ferris & P., 2019]b = load block, H(b) = hours in load block b.

Winter load duration curve for New Zealand

Load duration curve

[Ferris & P., 2019]b = load block, H(b) = hours in load block b.

Load duration curve as load blocks

Gemstone model detail

k = technology

Minimize fixed and expected variable costs.

P: min∑

k(Kkxk + Lkzk) +∑

t Eω[Z (t, ω)]s.t. Z (t, ω) =

∑b∈t H(b) (

∑k Ckyk(t, ω, b) + Vq(t, ω, b)) ,

xk ≤ uk ,zk ≤ xk + Uk ,

yk(t, ω, b) ≤ µk(t, ω, b)zk ,∑b∈t H(b)yk(t, ω, b) ≤ νk(t, ω)

∑b∈t H(b)zk + s(t − 1)− s(t),

q(t, ω, b) ≤ d(t, ω, b),d(t, ω, b) ≤

∑k yk(t, ω, b) + q(t, ω, b),

s(t) ≤ Szk ,x , z , y , q, s ≥ 0.

Operating costs are random

ω = scenario, t = season, b = load block containing H(b) hours.

P: min∑

k(Kkxk + Lkzk) +∑

t Eω[Z (t, ω)]s.t. Z (t, ω) =

∑b∈t H(b) (

∑k Ckyk(t, ω, b) + Vq(t, ω, b)),

∑b∈t H(b)zk + s(t − 1)− s(t),

q(t, ω, b) ≤ d(t, ω, b),d(t, ω, b) ≤

∑k yk(t, ω, b) + q(t, ω, b),

s(t) ≤ Szk ,x , z , y , q, s ≥ 0.

Capacity of wind and run-of-river is random in a season

ω = scenario, t = season, b = load block containing H(b) hours.

P: min∑

k(Kkxk + Lkzk) +∑

t Eω[Z (t, ω)]s.t. Z (t, ω) =

∑b∈t H(b) (

∑b∈t H(b)zk + s(t − 1)− s(t),

q(t, ω, b) ≤ d(t, ω, b),d(t, ω, b) ≤

∑k yk(t, ω, b) + q(t, ω, b),

s(t) ≤ Szk ,x , z , y , q, s ≥ 0.

Modeling stored hydro

s(t) = stored water at end of season t.

P: min∑

k(Kkxk + Lkzk) +∑

t Eω[Z (t, ω)]s.t. Z (t, ω) =

∑b∈t H(b) (

∑k Ckyk(t, ω, b) + Vq(t, ω, b)) ,

∑b∈t H(b)zk + s(t − 1)− s(t),

q(t, ω, b) ≤ d(t, ω, b),d(t, ω, b) ≤

∑k yk(t, ω, b) + q(t, ω, b),

s(t) ≤ Szk ,x , z , y , q, s ≥ 0.

Energy input from reservoir inflows is random in a season

ω = scenario, t = season, b = load block containing H(b) hours.s(t) = stored water at end of season t.

P: min∑

k(Kkxk + Lkzk) +∑

t Eω[Z (t, ω)]s.t. Z (t, ω) =

∑b∈t H(b) (

∑b∈t H(b)zk+s(t − 1)− s(t),

q(t, ω, b) ≤ d(t, ω, b),d(t, ω, b) ≤

∑k yk(t, ω, b) + q(t, ω, b),

s(t) ≤ Szk ,x , z , y , q, s ≥ 0.

Accounting for CO2 emissions

Some capacity xk , k ∈ N , is deemed non-renewable.

Generation gk(ω) =∑

∑b∈t H(b)yk(t, ω, b), emits βkgk(ω) tonnes.

For a choice of θ ∈ [0, 1], constraint is either:∑k∈N xk ≤ (1− θ)

∑k∈N xk(T )

(reduce non-renewable capacity compared with year T ),

[∑k∈N gk(ω)

]≤ (1− θ)

∑k∈N gk(ωT )

(reduce expected non-renewable generation compared with year T ),

Eω [∑

k βkgk(ω)] ≤ (1− θ)∑

k βkgk(ωT )(reduce expected CO2 emissions compared with year T ).

Emission KPIs

Some capacity xk , k ∈ N , is non-renewable.

Generation gk(ω) =∑

∑b∈t H(b)yk(t, ω, b), emits βkgk(ω) tonnes.

For a choice of θ ∈ [0, 1], constraint is either:∑k βkgk(ω) ≤ (1− θ)

∑k βkgk(ωT )

(constrain CO2 emissions almost surely ),

Pω [∑

k βkgk(ω) ≤ (1− θ)∑

k βkgk(ωT )] ≥ 1− α(constrain CO2 emissions with probability 1− α ),

Fω [∑

k βkgk(ω)] ≤ (1− θ)∑

k βkgk(ωT )(constrain risk-adjusted expected CO2 emissions ).

Assumptions for New Zealand in 2035

Huntly 500MW coal plant decommissioned. No new coal.

0.5% p.a. demand growth in residental and commercial load.

Additional demand (5.7 TWh) from transport electrification(assumes 0.25% EVs in 2019 becomes 50% EVs in 2035).

Additional demand (4.0 TWh) from process heat electrification(33% switch from coal/gas).

Electricity demand 39.2 TWh in 2017 becomes 53.6 TWh in 2035

16 wind scenarios × 13 hydrology scenarios = 208.

Can build run-of-river hydro, onshore wind, solar PV, somegeothermal, batteries, gas plant (CCGT and OCGT), CCGT withcarbon capture and storage (CCS).

Summary

1 Introduction

4 Results

CO2 emissions as constraint binds

Gemstone: increasing θ on CO2 constraints

Cost increase (2017 NZD M p.a.) as CO2 constraint binds

Gemstone: increasing θ on CO2 constraints

Effect of risk aversion

Risk aversion uses (1− λ)E[Z ] + λAVaR0.90(Z ), λ = 0, 0.5, 0.8.

Capacity mix: non-renewable capacity constraint

Gemstone: solutions as non-renewable capacity constrained

Capacity mix: non-renewable energy constraint

Gemstone: solutions as non-renewable energy constrained

Capacity mix: CO2 emission constraint

Gemstone: solutions as CO2 emissions constrained.

Capacity mix: increasing carbon tax

Gemstone: solutions as carbon tax increases.

Takeaways

Electricity systems have uncertainties at different timescales that we can approximate in a single model.Outcomes depend on definition of 100% renewableelectricity. Reduce nonrenewable capacity, expectednonrenewable energy, or expected CO2 emissions?Outcomes depend on CO2 emissions KPI. Constrainemissions on average, almost surely, with highprobability, risk-adjusted ?Getting to 100% is much harder than getting to 99%Risk averse social plan produces different technologymix.

Takeaways

What’s missing?

What is the optimal path to destination? Largeuncertainty over long time scales (e.g. technologyadvances, future costs of climate change). Multistageproblem gives options to adapt, delay or abandon.Multi-horizon scenario trees [Skar et al, 2016 ] integratetime scales. See Emerald, a multistage stochasticversion of Gemstone solved in JuDGE.jl.

WB83 - Stochastic and Robust Optimization in Energy

Systems

11:40-12:00 Anthony Downward, Applying Multi-stage

Stochastic Programming to Investment Planning for

Energy Systems.

What’s missing?

What is the optimal path to destination? Largeuncertainty over long time scales (e.g. technologyadvances, future costs of climate change). Multistageproblem gives options to adapt, delay or abandon.Multi-horizon scenario trees [Skar et al, 2016 ] integratetime scales. See Emerald, a multistage stochasticversion of Gemstone solved in JuDGE.jl.

WB83 - Stochastic and Robust Optimization in Energy

Systems

11:40-12:00 Anthony Downward, Applying Multi-stage

Stochastic Programming to Investment Planning for

Energy Systems.

Postscript: what happened?

Climate Change Response (Zero Carbon) Amendment Bill, May 2019.[http://www.legislation.govt.nz]

Summary

1 Introduction

4 Results

Competitive models with risk averse agents

Previous models assume a social planner. How shouldthis change in competitive markets?Even with assumed perfect competition and convexity,competitive outcomes may differ from socially optimaloutcomes, e.g. when agents are risk averse.Competitive investment with risk trading when agentshave coherent risk measures [Ehrenmann & Smeers, 2011,Ralph & Smeers, 2015, De Maere dAertrycke et al, 2018, Kok et al,2019 ]

TC83 - Policy-Enabling Models for the Power Sector II

12:05 - 12:25 Golbon Zakeri, Investment Under

Uncertainty and Risk in Competitive Electricity

Markets.

Competitive Risk Averse Model

Competing suppliers a ∈ A sell electricity at π(ω) and pay forexpected CO2 emissions at σ.

Pa(π,σ): min K a(xa) + Fa[Z a(ω)]

s.t. Z a(ω) =∑

k∈a(Ck − π(ω)yak (ω))

+σ∑

k∈a E[βkyk(ω)]

yak (ω) ≤ xak , k ∈ a,

yak (ω) ≥ 0, k ∈ a.

Competitive Risk Averse Model

Electricity consumer c pays for electricity at π(ω).blank

Pc : min Fc [Z c(ω)]

s.t. Z c(ω) = −(V − π(ω))(d(ω)− qc(ω))

qc(ω) ≥ 0.

Competitive Risk Averse MOPEC

Find electricity prices π(ω) and a CO2 price σ and actions (xa, y a),a ∈ A and qc so that

(xa, y a) solves Pa(π, σ);

qc solves Pc(π, σ);

0 ≤∑a∈A

∑k∈a

y ak (ω) + qc(ω)− d(ω) ⊥ π(ω) ≥ 0;

0 ≤ (1− θ)∑a∈A

∑k∈a

βkyak (ωT )− Eω

[∑a∈A

∑k∈a

βkyk(ω)

]⊥ σ ≥ 0.

Equilibrium CO2 prices with increasing risk aversion

θ = 0.7, F(Z ) = (1− λ)E[Z ] + λAVaR0.90(Z ), λ = 0, . . . , 0.7.

Trading risk recovers social optimum

Can recover risk averse social optimum if risk marketis complete.An Arrow-Debreu security (purchased in stage 1) forpays the holder $1 in scenario ω in stage 2.A contingent carbon credit (purchased in stage 1)entitles the holder to emit 1 tonne of CO2-e inscenario ω in stage 2.Arrow-Debreu securities complete the financial market.Expectation CO2 constraint can be satisfied in riskedequilibrium if agents trade contingent carbon credits.

Challenges

Solving competitive equilibrium problems withincomplete risk markets is generally difficult.Competitive equilibrium problems with incomplete riskmarkets can have multiple equilibia [Gerard et al, 2018].

Risk aversion complicates competitive capacity choices[Mays et al, 2019].

Net-zero CO2 emissions targets typically excludeconsumers, which favours importers ofcarbon-intensive products [Economist, October 19, 2019].

International cooperation: a role for IFORS?

Challenges

THE END

References

De Maere dAertrycke, G., Ehrenmann, A. and Smeers, Y. Investment with

incomplete markets for risk: The need for long-term contracts. Energy

Policy, 105, pp.571-583, 2017.

Dowson, O. and Kapelevich, L., SDDP. jl: a Julia package for Stochastic

Dual Dynamic Programming. Optimization Online, 2017

Downward, A. and Philpott,A.B., Infinite horizon SDDP. EPOC technical

report, 2019.

Ehrenmann, A. and Smeers, Y., Generation capacity expansion in a risky

environment: a stochastic equilibrium analysis. Operations Research, 59(6),

pp.1332-1346, 2011.

Ferris, M.C. and Philpott, A.B., 100% renewable electricity with storage,

EPOC technical report, 2019.

Fulton B. Security of Supply in the New Zealand Electricity Market,

University of Auckland Engineering Honours Thesis, 2018.

References

Kok, C., Philpott, A.B. and Zakeri, G., Value of transmission capacity in

electricity markets with risk averse agents, EPOC technical report, 2018.

Gerard, H., Leclere, V. and Philpott, A., On risk averse competitive

equilibrium. Operations Research Letters, 46(1), pp.19-26, 2018.

Mays, J., Morton, D. and O’Neill, R.P., Asymmetric Risk and Fuel

Neutrality in Capacity Markets, 2019.

Pereira, M.V. and Pinto, L.M., Multi-stage stochastic optimization applied

to energy planning. Mathematical programming, 52(1-3), pp.359-375, 1991.

Ralph, D. and Smeers, Y., Risk trading and endogenous probabilities in

investment equilibria. SIAM Journal on Optimization, 25(4), pp.2589-2611,

Skar, C., Doorman, G., Prez-Valds, G.A. and Tomasgard, A., A multi-horizon

stochastic programming model for the European power system, 2016.

All EPOC technical reports and this talk can be downloaded fromwww.epoc.org.nz

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