Content of presentation
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Classification of economic values
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Evaluation of the economic values of RE and flexible resources under risks
Classification of economic values
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Energy value
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Flexibility value
- Capacity value
- Balancing value
- Grid value
- Learning curves
Where do the values come from?
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There is no plausible future scenario where no energy is consumed.
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Therefore, the economic values of RE and flexible resources ultimately arise from the relative cost reduction compared with the alternative (remain heavily dependent on conventional energy resources).
Cost or value? A matter of perspective
Energy value
Energy value: concept
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Without RE and flexible resources, the techno-economic parameters of conventional energy sources (e.g. their fixed and variable costs) determine the optimal technology to provide for a certain level of electricity demand.
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For simplicity, let us assume that the marginal cost of providing an additional unit of electricity demand, \(mc\), is merely a function of the total power generation from all conventional energy sources.
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With RE in the power system, what needs to be provided in the transition period by the conventional energy sources is the residual (net) load, \(rl\), which is demand load minus the power output of RE.
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Under our assumption, \(mc \equiv mc(rl)\), and it is also monotonically increasing.
Energy value: derivation
Given a known time series of capacity factor for the RE, \(cf(t)\), we have
$$rl(cap, t) = dl(t) - cap \cdot cf(t)$$where \(cap\) is the installed capacity of the RE technology.
The marginal energy value of an additional unit of RE capacity will then be
$$mev(cap) \equiv \int^T_0 mc(rl(cap, t)) \cdot cf(t) dt$$where \(T\) is usually set to 1 year.
Energy value: illustration
Marginal energy value decreases
Mathematical derivation:
$$ \partial_{cap} mev = \int^T_0 mc' \cdot \partial_{cap} rl \cdot cf(t) dt $$$$ = -\int^T_0 mc' \cdot \left( cf(t) \right)^2 dt \leq 0 $$
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Intuition behind the math: since the same type of RE power plants tend to have positively correlated capacity factor profiles, when they dominate the power system, more of their power output would occur when residual load (therefore marginal energy value) is lower.
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Generally speaking, solar and wind have negatively correlated capacity factor profiles, making them complementary with each other.
Flexibility value
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Capacity value refers to the ability of the resources to reliably reduce the peak residual electricity demand at a certain time period.
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Balancing value refers to the ability of the resources to provide controlled deviation from its schedule so to enhance reliability and stability on the global (transmission) level.
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Grid value refers to the ability of the resources to provide controlled deviation from its schedule so to enhance reliability and stability on the local (distribution, microgrid) level.
Capacity value: concept
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For simplicity, let us focus on the capacity value.
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The power output of many RE technologies are variable and probabilistic by default. Let us focus on the variable part in the following discussion.
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The marginal capacity value, \(mcv\), of a RE technology is the capacity factor of that technology when peak residual load occurs.
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As the peak residual load can only shifts toward time periods with lower capacity factor values, the \(mcv\) of a RE technology decreases as more of the same technology is deployed.
Marginal capacity value decreases
Capacity value: actual data
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For example, the \(mcv\) of solar in Taiwan has dropped to 0 in 2025, since peak residual load occurred on a late summer evening.
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Nevertheless, the total capacity value of RE technologies was almost 3 GW in 2025.
Capacity value: synergies
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While RE technologies are not suitable for providing capacity values at a large scale, their impact on the residual load makes complementary flexible resources more cost-effective.
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To see why, let us consider a battery storage system with a marginal unit of charge / discharge power output. Let us consider how much volume of energy storage is needed for this BESS to effectively replace a marginal unit of conventional power plant capacity.
Capacity value: synergies (illustration)
Capacity value: long term synergies
Capacity value: synergies (conclusion)
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In short, with more RE on the power system, it would take less energy storage volume for the BESS to replace a marginal unit of conventional power plant capacity (less investment cost).
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Also, RE reduces marginal cost of electricity during RL valley, making charging of BESS cheaper (less variable cost).
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Both effects make BESS more cost-effective.
Learning curve
Learning curve: concept
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The fact that the costs of RE and many flexible resources reduce as more of them are deployed means that there exist additional economic values not accounted for from the analysis based on short-term operation of the energy system.
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Future reduction of installation costs because of today’s deployment should therefore be considered when discussing the value of RE and flexible resources.
Learning curve: toy example
Let us assume that the techno-economic parameters of conventional energy sources remain the same and consider the following two cases:
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Case 0: the investment cost of the same RE power plant is also fixed
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Case 1: the investment cost of the same RE power plant reduces as more of the same technology is deployed
Learning curve: case 0
In the first case, we can obtain an optimal steady state capacity \(cap^*\) for the long-term cost optimization problem by setting the depreciated marginal energy values\({}^{1}\) of the RE technology equal to its marginal investment cost \(mic\) over its life span \(Y\):
$$ \sum^Y_{y=0} mev(cap^*) \exp(-ry) = mic $$\({}^{1}\) For simplicity we shall ommit flexible values in the discussion here.
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As a steady state solution, \(cap^*\) will be a constant. In other words, without the consideration of the learning curve, there will be no more long-term temporal dynamics in RE investment once the optimal capacity is reached.
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More specifically, whatever amount of RE capacity is retired at a year, will be replaced with the exact amount of capacity at that year.
Learning curve: case 1
$$ cap(y) = cap(y-1) + k(y) - k(y - Y - 1) $$$$ = k(y - Y) + ... + k(y) $$
$$ a(y) = a(y - 1) + k(y) = k(0) + ... + k(y) $$$$ mic(a(y)) = c_0 \left( a(y) \right)^{-\alpha} $$
where \(cap(y)\) is the capacity of RE at year y, \(a(y)\) the accumulated built capacity of RE at year y, and \(\alpha \geq 0\) a parameter for the learning curve.
Learning curve: comparison between case 0 and case 1
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At optimal RE capacity, case 1 has lower \(mev\) at any given time.
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Since \(mev\) monotonically decreases, this means that the optimal RE capacity is higher in case 1 at any given time.
Evaluation of the economic values of RE and flexible resources under risks
Why evaluation of risks is important
The investment of energy and flexible resources contains many types of risks, including:
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Schedule delay of a project
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Cost overrun of a project
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Stochastic price fluctuation in related markets
Building blocks towards fully accounting for the risks
We will gradually advance the methodology until the risks can be fully accounted for:
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Deterministic NPV
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Probabilistic NPV
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Real options analysis
Toy example for NPV: two options of solar PV project
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Option 1: build consecutively 2 solar PV power plants, 0.5 MW each
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Option 2: build a 1 MW solar PV power plant
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Basic assumptions:
- On average, each power plant in option 1 takes a year to complete, while the power plant in option 2 takes 2 years to complete.
- Option 2 has lower fixed cost per capacity
Deterministic NPV
Assume:
- The upfront investment cost for is 1 unit for each power plant in option 1 and 1.5 unit for the power plant in option 2.
- Depreciation factor \(r = 0.03\) per year.
- Marginal energy value is 0.2 unit per MW per year.
- Life span for each power plant is 20 years.
Deterministic NPV: Option 1
The NPV for building a power plant in option 1 now is
$$ NPV_0 = 0.1 \int^{21}_1 \exp(-0.03t) dt - 1 $$$$ = \frac{10}{3}\exp(-0.03) \left(1 - \exp(-0.6) \right) - 1 $$$$ = 0.4595124 $$If we build the first power plant now and the second power plant 1 year later, the total NPV for option 1 would be
$$ NPV = NPV_0 (1 + \exp(-0.03)) $$$$ = 0.9054442 $$
Deterministic NPV: Option 2
The NPV for building the power plant in option 2 now is
$$ NPV = 0.2 \int^{22}_2 \exp(-0.03t) dt - 1.5 $$$$ = 1.332755 $$
With deterministic NPV, option 2 is more valuable than option 1.
Probabilistic NPV
In addition to assumptions in the deterministic NPV, let us now take into account the risk of schedule delay and cost overrun:
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The construction time of the power plants follows a gamma distribution.
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Each year of construction incurs an additional \(10\%\) investment cost compared with the upfront investment cost.
Probabilistic NPV: construction time distribution
Probabilistic NPV: option 1
The present value of the profit flow of a just completed power plant is
$$ PF_0 = \frac{cap_1 \cdot mev}{r} (1 - \exp(-rY)) $$The expected NPV of a power plant being built from now is
$$ NPV_0 = \int^{\infty}_0 \exp(-rt) f_1(t) \:\cdot $$$$ \left( PF_0 - 0.1 c_{0, 1} t \right) dt - c_{0, 1} $$Remark: This is a fine-tuned case where closed-form solution exists (Laplace transform of polynomials). Usually, only numerical calculations are possible.
If we build the first power plant now, wait for it to be completed, and then build the second power plant, the total NPV for option 1 would be
$$ NPV = \int^{\infty}_0 \exp(-rt) f_1(t) $$$$ \left( NPV_0 + PF_0 - 0.1 c_{0, 1} t \right) dt - c_{0, 1} $$$$ = NPV_0 \left( 1 + \int^{\infty}_0 \exp(-rt) f_1(t) dt \right) $$Probabilistic NPV: comparison
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With these assumptions, the NPV value of option 1 (0.7177266) becomes closer to that of option 2 (1.055536).
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Main reason: the risk of cost overrun for the larger project in option 2 due to schedule delay is greater.
Cost overrun risks
| Project type | Mean cost overrun (%) | Projects with \(\geq\:50\%\) overruns (%) | Mean overruns of projects in tail (%) |
|---|---|---|---|
| Solar | 1 | 2 | 50 |
| Transmission | 8 | 4 | 166 |
| Wind | 13 | 7 | 97 |
| Fossil thermal | 16 | 14 | 109 |
| Hydro (dam) | 75 | 37 | 186 |
| Nuclear | 120 | 55 | 204 |
| Nuclear waste storage | 238 | 48 | 427 |
Note: Tail are projects with \(\geq\:50\%\) overruns. Data from Flyvbjerg database.
Real options analysis (stochastic dynamic programming)
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While probabilistic NPV already account for some risks, a crucial degree of freedom is missing in it: the ability for the investor to postpone the decision and invest in the future.
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This makes sense when the market values and investment costs of the RE and flexible resources are also stochastic.
ROA: illustration
For longer time span and more possible future trajectories, Monte Carlo methods are usually used in ROA.
ROA: case study
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ROA conducted on a Norwegian local energy community to determine whether and when to invest in BESS and solar PV.
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Risks considered:
- spot and balancing market prices
- investment cost of PV and BESS
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Uncertainties considered:
- regulatory uncertainties: whether the LEC can participated in various balancing markets
Relevant findings
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BESS hedge against price risks in the markets and make the profit flow less volatile. This reduces its real options value.
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On its own, solar PV has negative NPV, but due to expected lower investment costs in the future it has high ROV.
Interyear volatility in annual savings, FCR and spot prices for the ‘‘BA’’ and ‘‘BA: No FCR’’ cases.
Investigating the added value of ROV.
Reflection
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According to ROA, the LEC should wait longer until cost of PV reduces further.
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However, cost of PV can only be reduced further with more deployment (as discussed previously in the learning curve section) in society.
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The misalignment of micro and social interests suggests the necessity of supporting policies for the roll-out of RE and flexible resources.