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corrected max power gradient docs
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ojdo committed Nov 27, 2015
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Expand Up @@ -990,7 +990,7 @@ Transmission Economical Parameters

**Tranmission Depreciation Period**, :math:`z_{af}`, (a): The parameter :math:`z_{af}` represents the depreciation period of a transmission :math:`f` transferring commodities through an arc :math:`a`. The depreciation period of gives the economic lifetime (more conservative than technical lifetime) of a transmission investment. The unit of this parameter is €/ (MW a). The related section for this parameter in the spreadsheet can be found under the "Transmission" sheet. Here each row represents another transmission :math:`f` transferring commodities through an arc :math:`a` and the thirteenth column with the header label "depreciation" represents the parameters :math:`z_{af}` of the corresponding transmission :math:`f` and arc :math:`a` combinations.

**Annualised Transmission Capacity Investment Costs**, :math:`k_{af}^\text{inv}`, ``m.transmission.loc[t]['inv-cost'] * m.transmission.loc[t]['annuity-factor']``: The parameter :math:`k_{af}^\text{inv}` represents the annualised investment cost for adding one unit new transmission capacity to a transmission :math:`f` transferring commodities through an arc :math:`a``. This parameter is derived by the product of annuity factor :math:`AF` and the investment cost for one unit of new transmission capacity of a transmission :math:`f` running through an arc :math:`a`, which is to be given as an input parameter by the user. The unit of this parameter is €/(MW a). The related section for the transmission capacity investment cost in the spreadsheet can be found under the "Transmission" sheet. Here each row represents another transmission :math:`f` transferring commodities through an arc :math:`a` and the sixth column with the header label "inv-cost" represents the transmission capacity investment cost of the corresponding transmission :math:`f` and arc :math:`a` combinations.
**Annualised Transmission Capacity Investment Costs**, :math:`k_{af}^\text{inv}`, ``m.transmission.loc[t]['inv-cost'] * m.transmission.loc[t]['annuity-factor']``: The parameter :math:`k_{af}^\text{inv}` represents the annualised investment cost for adding one unit new transmission capacity to a transmission :math:`f` transferring commodities through an arc :math:`a`. This parameter is derived by the product of annuity factor :math:`AF` and the investment cost for one unit of new transmission capacity of a transmission :math:`f` running through an arc :math:`a`, which is to be given as an input parameter by the user. The unit of this parameter is €/(MW a). The related section for the transmission capacity investment cost in the spreadsheet can be found under the "Transmission" sheet. Here each row represents another transmission :math:`f` transferring commodities through an arc :math:`a` and the sixth column with the header label "inv-cost" represents the transmission capacity investment cost of the corresponding transmission :math:`f` and arc :math:`a` combinations.

**Annual Transmission Capacity Fixed Costs**, :math:`k_{af}^\text{fix}`, ``m.transmission.loc[t]['fix-cost']``: The parameter :math:`k_{af}^\text{fix}` represents the fix cost per one unit capacity of a transmission :math:`f` transferring commodities through an arc :math:`a`, that is charged annually. The unit of this parameter is €/(MWh a). The related section for this parameter in the spreadsheet can be found under the "Transmission" sheet. Here each row represents another transmission :math:`f` transferring commodities through an arc :math:`a` and the seventh column with the header label "fix-cost" represents the parameters :math:`k_{af}^\text{fix}` of the corresponding transmission :math:`f` and arc :math:`a` combinations.

Expand Down Expand Up @@ -1713,11 +1713,11 @@ In script ``urbs.py`` the constraint process throughput by capacity rule is defi
def res_process_throughput_by_capacity_rule(m, tm, sit, pro):
return (m.tau_pro[tm, sit, pro] <= m.cap_pro[sit, pro])

**Process Throughput Gradient Rule**: The constraint process throughput gradient rule limits the process power gradient :math:`\{PG}_{vpt}`. This constraint prevents processes from exceeding their maximal possible power gradient. The constraint states that absolute power gradient must be less than or equal to the maximal power gradient :math:`\overline{PG}_{vp}`. In mathematical notation this is expressed as:
**Process Throughput Gradient Rule**: The constraint process throughput gradient rule limits the process power gradient :math:`\left| \tau_{vpt} - \tau_{vp(t-1)} \right|`. This constraint prevents processes from exceeding their maximal possible change in activity from one time step to the next. The constraint states that absolute power gradient must be less than or equal to the maximal power gradient :math:`\overline{PG}_{vp}` parameter (scaled to capacity and by time step duration). In mathematical notation this is expressed as:

.. math::
\forall v\in V, p\in P, t\in T_m\colon \qquad & \qquad \{PG}_{vpt} &\leq \overline{PG}_{vp}
\forall v\in V, p\in P, t\in T_m\colon \qquad & \qquad \left| \tau_{vpt} - \tau_{vp(t-1)} \right| &\leq \kappa_{vp} \overline{PG}_{vp} \Delta t
In script ``urbs.py`` the constraint process throughput gradient rule is defined and calculated by the following code fragment:
::
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