Add section on flexible assets to docs #1111
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@@ -149,25 +149,183 @@ time-varying availability limits. For all \\( a \in \mathbf{A}^{std}, r, t \\): | |
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| \\[ act[a,r,t] = capacity[a,r]\\,cap2act[a]\\,avail_{EQ}[a,t]\\,duration[t] \\] | ||
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| ## B. Flexible Assets (\\( a \in \mathbf{A}^{flex} \\)) | ||
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| **Purpose:** This section defines the operational characteristics of flexible assets, which can | ||
| adjust their input consumption mix and/or output product shares, governed by an overall process | ||
| efficiency. The generic activity variable \\( act[a,r,t] \\) (linked to the asset's physical \\( | ||
| capacity[a,r] \\)) is connected to the scale of this flexible conversion process via a reference | ||
| output parameter. It is assumed that SVD commodities cannot be efficiency-constrained or auxiliary | ||
| inputs to these assets. | ||
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| ### B.1. Asset-Specific Sets (Defined for each flexible asset \\( a \in \mathbf{A}^{flex} \\)) | ||
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| These sets categorize the commodities involved in the flexible asset's operation. | ||
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| - \\( \mathbf{C}^{eff\\_ in}_a \subseteq (\mathbf{C}^{\mathrm{SED}} \cup \mathbf{C}^{\mathrm{OTH}}) | ||
| \\): Set of input commodities for asset \\( a \\) whose combined energy or mass content is subject | ||
| to the main process efficiency \\( \eta[a] \\). | ||
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| - \\( \mathbf{C}^{eff\\_ out}_a \subseteq \mathbf{C} \\): Set of main output commodities from asset | ||
| \\( a \\) whose combined energy or mass content is determined by \\( \eta[a] \\) and the processed | ||
| inputs. | ||
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| - \\( \mathbf{C}^{aux\\_ in}_a \subseteq (\mathbf{C}^{\mathrm{SED}} \cup \mathbf{C}^{\mathrm{OTH}}) | ||
| \\): Set of auxiliary input commodities for asset \\( a \\) (e.g., water, catalysts) whose | ||
| consumption is typically proportional to the main activity \\( act[a,r,t] \\) but which are not | ||
| part of the primary energy/mass balance for the efficiency calculation. | ||
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| - \\( \mathbf{C}^{aux\\_ out}_a \subseteq \mathbf{C} \\): Set of auxiliary output commodities for | ||
| asset \\( a \\) (e.g., specific emissions, waste streams) whose production is typically | ||
| proportional to \\( act[a,r,t] \\) but which are not counted in the efficiency calculation for the | ||
| primary products. | ||
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| ### B.2. Parameters (for \\( a \in \mathbf{A}^{flex} \\)) | ||
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| These parameters define the technical and economic behavior of flexible assets. | ||
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| - \\( \eta[a] \\): The overall process efficiency (\\( \in (0,1] \\)) of flexible asset \\( a \\), | ||
| relating total common units of outputs in \\( \mathbf{C}^{eff\\_out}_a \\) to inputs in \\( | ||
| \mathbf{C}^{eff\\_in}_a \\). | ||
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| - \\( factor_{CU}[c] \\): A commodity-specific factor to convert its native physical units (e.g., | ||
| tonnes, m³) to a common unit (e.g., MWh of energy content, or tonnes of mass if it's a mass | ||
| balance) used for consistent efficiency and input/output share calculations. | ||
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| - \\( RefEffOutPerAct[a] \\): Reference Total Efficiency-constrained Output per unit of Activity. | ||
| This crucial parameter defines the total quantity of efficiency-constrained outputs (summed in | ||
| common units using \\( factor_{CU}[c] \\)) that are produced when asset \\( a \\) operates at one | ||
| unit of its generic activity level \\( act[a,r,t] \\). | ||
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| - \\( minInputShare[a,c] \\) (for \\( c \in \mathbf{C}^{eff\\_ in}_a \\)): Minimum fractional share | ||
| of input commodity \\( c \\) (in common units) relative to the total efficiency-constrained input | ||
| (in common units). | ||
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| - \\( maxInputShare[a,c] \\) (for \\( c \in \mathbf{C}^{eff\\_ in}_a \\)): Maximum fractional share | ||
| for input \\( c \\). | ||
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| - \\( minOutputShare[a,c] \\) (for \\( c \in \mathbf{C}^{eff\\_ out}_a \\)): Minimum fractional | ||
| share of output commodity \\( c \\) (in common units) relative to the total efficiency-constrained | ||
| output. | ||
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| - \\( maxOutputShare[a,c] \\) (for \\( c \in \mathbf{C}^{eff\\_ out}_a \\)): Maximum fractional | ||
| share for output \\( c \\). | ||
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| - \\( coeff_{aux\\_ in}[a,c] \\) (for \\( c \in \mathbf{C}^{aux\\_ in}_a \\)): Quantity of auxiliary | ||
| input \\( c \\) consumed per unit of \\( act[a,r,t] \\). | ||
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| - \\( coeff_{aux\\_ out}[a,c] \\) (for \\( c \in \mathbf{C}^{aux\\_ out}_a \\)): Quantity of | ||
| auxiliary output \\( c \\) produced per unit of \\( act[a,r,t] \\). | ||
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| ### B.3. Decision Variables (for \\( a \in \mathbf{A}^{flex} \\)) | ||
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| These variables represent the operational choices for flexible assets. | ||
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| - \\( act[a,r,t]\ge0 \\): Generic activity level of flexible asset \\( a \\) (linked to its \\( | ||
| capacity[a,r] \\)). | ||
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| - \\( InputSpec[a,c,r,t]\ge0 \quad \forall c \in \mathbf{C}^{eff\\_ in}\_a \\): Actual amount of | ||
| efficiency-constrained input commodity \\( c \\) consumed by asset \\( a \\) in region \\( r \\), | ||
| time \\( t \\) (in its native physical units). | ||
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| - \\( OutputSpec[a,c,r,t]\ge0 \quad \forall c \in \mathbf{C}^{eff\\_ out}\_a \\): Actual amount of | ||
| efficiency-constrained output commodity \\( c \\) produced by asset \\( a \\) in region \\( r \\), | ||
| time \\( t \\) (in its native physical units). | ||
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There was a problem hiding this comment. In the decision-variable definitions, the set qualifiers use |
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| ### B.4. Objective Contribution (for \\( a \in \mathbf{A}^{flex} \\)) | ||
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| The cost contribution from flexible assets includes costs related to their generic activity, | ||
| specific costs for efficiency-constrained inputs and outputs (if defined separately from system | ||
| commodity values), and costs/revenues for auxiliary inputs and outputs. | ||
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| \\[ | ||
| \begin{aligned} | ||
| &act[a,r,t] \cdot cost\_{var}[a,r,t] \\\\ | ||
| &+ \sum\_{c \in \mathbf{C}^{eff\\_ in}\_a} InputSpec[a,c,r,t] \cdot cost\_{input}[a,c] \\\\ | ||
| &+ \sum\_{c \in \mathbf{C}^{eff\\_ out}\_a} OutputSpec[a,c,r,t] \cdot cost\_{output}[a,c] \\\\ | ||
| &+ \sum\_{c \in \mathbf{C}^{aux\\_ in}\_a} (act[a,r,t] \cdot coeff\_{aux\\_ in}[a,c]) | ||
| \cdot cost\_{input}[a,c] \\\\ | ||
| &+ \sum\_{c \in \mathbf{C}^{aux\\_ out}\_a} (act[a,r,t] \cdot coeff\_{aux\\_ out}[a,c]) | ||
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| \cdot cost\_{output}[a,c] \\\\ | ||
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There was a problem hiding this comment. In the B.4 objective expression, the summation index sets are written with |
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| \end{aligned} | ||
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There was a problem hiding this comment. The flexible-asset objective contribution is presented without the outer summations over assets/regions/time. As written, it reads like a single (a,r,t) term rather than the contribution to the total objective (contrast with A.3 which includes |
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| \\] | ||
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| ### B.5. Constraints (for \\( a \in \mathbf{A}^{flex}, r \in \mathbf{R}, t \in \mathbf{T} \\)) | ||
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| These rules govern the internal operation and conversion process of flexible assets. Let \\( | ||
| ActualTotalEffOutputCU[a,r,t] = RefEffOutPerAct[a] \cdot act[a,r,t] \\) (This is the total | ||
| efficiency-constrained output in common units). Let \\( ActualTotalEffInputCU[a,r,t] = | ||
| (RefEffOutPerAct[a] / \eta[a]) \cdot act[a,r,t] \\) (This is the total efficiency-constrained input | ||
| in common units, derived from the output and efficiency). | ||
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| - **Capacity & Availability:** Standard capacity and availability constraints (as in A.4) apply to | ||
| the generic activity variable \\( act[a,r,t] \\) of the flexible asset. | ||
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| - **Total Efficiency-Constrained Input Definition:** The sum of all specific efficiency-constrained | ||
| inputs, when converted to common units by \\( factor_{CU}[c] \\), must equal the total | ||
| efficiency-constrained input derived from \\( act[a,r,t] \\) and the asset's efficiency: | ||
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| \\[ | ||
| \sum\_{c \in \mathbf{C}^{eff\\_ in}\_a} InputSpec[a,c,r,t] \cdot factor\_{CU}[c] | ||
| = ActualTotalEffInputCU[a,r,t] | ||
| \\] | ||
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There was a problem hiding this comment. The efficiency-constrained input definition equation uses |
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| - **Total Efficiency-Constrained Output Definition:** Similarly, the sum of all specific main | ||
| outputs (in common units) must equal the total defined by \\( act[a,r,t] \\) and the reference | ||
| output parameter: | ||
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| \\[ | ||
| \sum\_{c \in \mathbf{C}^{eff\\_out}\_a} OutputSpec[a,c,r,t] \cdot factor\_{CU}[c] | ||
| = ActualTotalEffOutputCU[a,r,t] | ||
| \\] | ||
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There was a problem hiding this comment. The efficiency-constrained output definition equation uses |
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| - **Input Share Constraints** (for each \\( c \in \mathbf{C}^{eff\\_in}_a \\)): Ensure that each | ||
| individual efficiency-constrained input (in common units) stays within its defined minimum (\\( | ||
| minInputShare[a,c] \\)) and maximum (\\( maxInputShare[a,c] \\)) fractional share of the \\( | ||
| ActualTotalEffInputCU[a,r,t] \\). | ||
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| \\[ | ||
| \begin{aligned} | ||
| InputSpec[a,c,r,t] \cdot factor\_{CU}[c] | ||
| &\ge minInputShare[a,c] \cdot ActualTotalEffInputCU[a,r,t] \\\\ | ||
| InputSpec[a,c,r,t] \cdot factor\_{CU}[c] | ||
| &\le maxInputShare[a,c] \cdot ActualTotalEffInputCU[a,r,t] | ||
| \end{aligned} | ||
| \\] | ||
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| - **Output Share Constraints** (for each \\( c \in \mathbf{C}^{eff\\_out}_a \\)): Ensure that each | ||
| individual efficiency-constrained output (in common units) stays within its defined minimum (\\( | ||
| minOutputShare[a,c] \\)) and maximum (\\( maxOutputShare[a,c] \\)) fractional share of the \\( | ||
| ActualTotalEffOutputCU[a,r,t] \\). | ||
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| \\[ | ||
| \begin{aligned} | ||
| OutputSpec[a,c,r,t] \cdot factor\_{CU}[c] | ||
| &\ge minOutputShare[a,c] \cdot ActualTotalEffOutputCU[a,r,t] \\\\ | ||
| OutputSpec[a,c,r,t] \cdot factor\_{CU}[c] | ||
| &\le maxOutputShare[a,c] \cdot ActualTotalEffOutputCU[a,r,t] | ||
| \end{aligned} | ||
| \\] | ||
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| ## C. Full Model Construction | ||
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| > Note: This section includes references to many features that are not described elsewhere in this | ||
| > document or implemented yet (e.g. region-to-region trade), but these are included for | ||
| > completeness. This represents the roadmap for future MUSE2 development. | ||
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| This section describes how all preceding components are integrated to form the complete dispatch | ||
| optimisation problem. | ||
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| ### C.1. Objective Function | ||
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| The overall objective is to minimise the total system cost, which is the sum of all operational | ||
| costs from assets (standard and flexible), financial impacts from policy scopes (taxes minus | ||
| credits), costs of inter-regional trade, costs of pool-based trade, and importantly, the high | ||
| economic penalties associated with any unserved demand for critical commodities: | ||
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| \\[ | ||
| \begin{aligned} | ||
| \text{Minimise: } &(\text{Core Asset Operational Costs from A.3 and B.4}) \\\\ | ||
| &+ \sum_{c \in \mathbf{C}^{VoLL},r,t} UnmetD[c,r,t] \cdot VoLL[c,r] | ||
| \quad \text{(Penalty for Unserved Demand)} | ||
| \end{aligned} | ||
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There was a problem hiding this comment. There's a discrepancy between the descriptive text and the actual objective function equation. The text (lines 320-323) states that the objective includes "financial impacts from policy scopes (taxes minus credits), costs of inter-regional trade, costs of pool-based trade", but the equation (lines 327-328) only includes "Core Asset Operational Costs from A.3 and B.4" and the penalty for unserved demand. Either the descriptive text should be updated to match the equation (removing mentions of scope policies, R2R trade, and pool trade), or the equation should include these terms.
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There was a problem hiding this comment. Yeah, the equation is currently incomplete. We haven't added these features yet.
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@@ -176,22 +334,19 @@ commodities: | |
| Note that the unmet demand variables (\\( UnmetD[c,r,t] \\)) are normally not included in the | ||
| optimisation and are currently only used to diagnose the source of errors when running the model. | ||
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| ### C.2. Constraints | ||
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| The complete set of constraints that the optimisation must satisfy includes: | ||
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| - Capacity & Availability constraints for all assets \\( a \in \mathbf{A} \\) | ||
| (as per [A.4] and [B.5]) | ||
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| - [Flexible Asset operational constraints][B.5] | ||
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There was a problem hiding this comment. The constraints list is currently redundant: the first bullet already references B.5, and the next bullet links to B.5 again. Consider making the first bullet reference only A.4 for capacity/availability, and keep a separate bullet for the remaining flexible-asset operational constraints (B.5), or otherwise remove the duplication. |
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| [A.4]: #a4-constraints-capacity--availability-for-standard-assets--a-in-mathbfastd- | ||
| [B.5]: #b5-constraints-for--a-in-mathbfaflex-r-in-mathbfr-t-in-mathbft- | ||
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| #### Demand Satisfaction for \\( c\in \mathbf{C}^{\mathrm{SVD}} \\) | ||
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| These constraints ensure that exogenously defined final demands for SVDs are met in each region \\( | ||
| r \\) and time slice \\( t \\), or any shortfall is explicitly accounted for. | ||
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@@ -218,7 +373,7 @@ Else (if SVD \\( c \\) must be strictly met and is not included in \\( \mathbf{C | |
| \ge demand[r,c] \times timeslice\\_ share[c,t] | ||
| \\] | ||
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| #### Commodity Balance for \\( c\in \mathbf{C}^{\mathrm{SED}} \\) | ||
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| These constraints ensure that for all intermediate SED commodities, total supply equals total demand | ||
| within each region \\( r \\) and for each balancing period defined by \\( balance\\_ level[c,r] \\) | ||
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@@ -238,8 +393,8 @@ other regions). | |
| \left( | ||
| \begin{cases} | ||
| OutputSpec[a,c,r,t] & \text{if } c \in \mathbf{C}^{eff\\_out}\_a \\\\ | ||
| act[a,r,t] \cdot coeff\_{aux\\_out}[a,c] & \text{if } c \in \mathbf{C}^{aux\\_out}\_a \\\\ | ||
| 0 & \text{otherwise} | ||
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There was a problem hiding this comment. In the flex-asset production case distinction, the set names use |
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| \end{cases} | ||
| \right) | ||
| && \text{(Flex Asset Production)} \\\\ | ||
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Math formatting is still inconsistent for names like
eff\_in/eff\_out: earlier you use the spaced form noted at the top of the file (e.g.,\mathbf{C}^{eff\_ in}_a,\mathbf{C}^{eff\_ out}_a), but here it switches to\mathbf{C}^{eff\_out}_a/\mathbf{C}^{eff\_in}_a. Given the mdbook rendering note, it’s safer to standardize on one form throughout (preferably the spaced version used elsewhere in this document).