zen_garden.model.technology.technology

Defines the parameters, variables and constraints that hold for all technologies. The class takes the abstract optimization model as an input, and returns the parameters, variables and constraints that hold for all technologies.

Classes

Technology(technology, optimization_setup)	Defines parameters, variables and constraints holding for all technologies.
TechnologyRules(optimization_setup)	Rules for the Technology class.

class zen_garden.model.technology.technology.Technology(technology: str, optimization_setup)

Defines parameters, variables and constraints holding for all technologies.

__init__(technology: str, optimization_setup)

Init generic technology object.

Parameters:

• technology – technology that is added to the model

• optimization_setup – The OptimizationSetup the element is part of

add_new_capacity_addition_tech(capacity_addition: Series, capex: Series, step_horizon: list)

Adds the newly built capacity to the existing capacity.

Parameters:

• capacity_addition – pd.Series of newly built capacity of technology

• capex – pd.Series of capex of newly built capacity of technology

• step_horizon – current horizon step

add_new_capacity_investment(capacity_investment: Series, step_horizon: list)

Adds the newly invested capacity to the list of invested capacity.

Parameters:

• capacity_investment – pd.Series of newly built capacity of technology

• step_horizon – optimization time step

calculate_capex_of_capacities_existing(storage_energy=False)

This method calculates the annualized capex of the existing capacities.

Parameters:

storage_energy – boolean if energy storage

Returns:

capex of existing capacities

calculate_capex_of_single_capacity(*args)

Calculates annualized capex of existing capacity, implemented in child class.

Parameters:

args – arguments

calculate_fraction_of_year()

Calculate fraction of year.

classmethod construct_constraints(optimization_setup)

Constructs the Constraints of the class <Technology>.

Parameters:

optimization_setup – The OptimizationSetup

classmethod construct_params(optimization_setup)

Constructs the pe.Params of the class <Technology>.

Parameters:

optimization_setup – The OptimizationSetup

classmethod construct_sets(optimization_setup)

Constructs the pe.Sets of the class <Technology>.

Parameters:

optimization_setup – The OptimizationSetup

classmethod construct_vars(optimization_setup)

Constructs the pe.Vars of the class <Technology>.

Parameters:

optimization_setup – The OptimizationSetup

classmethod get_available_existing_quantity(optimization_setup, tech, capacity_type, loc, year, type_existing_quantity)

Gets the existing quantity of ‘tech’ at investment time step ‘time’.

returns existing quantity of ‘tech’, that is still available at invest time step ‘time’. Either capacity or capex.

Parameters:

• optimization_setup – The OptimizationSetup the element is part of

• tech – name of technology

• capacity_type – type of capacity

• loc – location (node or edge) of existing capacity

• year – current yearly time step

• type_existing_quantity – capex or capacity

Returns:

existing_quantity: existing capacity or capex of existing capacity

classmethod get_existing_quantity(optimization_setup, type_existing_quantity)

Get existing capacities of all technologies.

Parameters:

• optimization_setup – The OptimizationSetup the element is part of

• type_existing_quantity – capacity or cost_capex_overnight

Returns:

The existing capacities

classmethod get_first_lifetime_time_step(optimization_setup, tech, year, use_depreciation_time=False)

Get first time step of active capacity of technology.

Returns the first time step within the lifetime or depreciation time of the technology, i.e., the earliest past time step whose installed capacity is still active at the given time step.

Parameters:

• optimization_setup – OptimizationSetup the technology is part of

• tech – name of the technology

• year – current yearly time step

• use_depreciation_time – boolean indicating whether to use depreciation time instead of standard lifetime for capacity calculation

Returns:

first time step where capacity or investment is still valid

classmethod get_if_capacity_still_existing(optimization_setup, tech, year, loc, id_capacity_existing)

Returns boolean if capacity still exists at yearly time step ‘year’.

Parameters:

• optimization_setup – The optimization setup to add everything

• tech – name of technology

• year – yearly time step

• loc – location

• id_capacity_existing – id of existing capacity

Returns:

boolean if still existing

classmethod get_investment_time_step(optimization_setup, tech, year)

Returns investment time step of technology, considering construction time.

returns investment time step of technology, i.e., the time step in which the technology is invested considering the construction time.

Parameters:

• optimization_setup – The optimization setup to add everything

• tech – name of technology

• year – yearly time step

Returns:

investment time step

classmethod get_lifetime_range(optimization_setup, tech, year, use_depreciation_time=False)

Get active year range of technology: either lifetime or depreciation time.

Parameters:

• optimization_setup – OptimizationSetup the technology is part of

• tech – name of the technology

• year – yearly time step

• use_depreciation_time – boolean indicating whether to use depreciation time instead of lifetime, namely for CAPEX calculation

Returns:

lifetime or depreciation time range of technology

store_carriers()

Retrieves and stores information on reference.

store_input_data()

Retrieves and stores input data for element as attributes.

Each Child class overwrites method to store different attributes.

class zen_garden.model.technology.technology.TechnologyRules(optimization_setup)

Rules for the Technology class.

__init__(optimization_setup)

Inits the rules.

Parameters:

optimization_setup – OptimizationSetup of the element

constraint_carbon_emissions_technology_total()

Calculate total carbon emissions of each technology.

\[E_y^{\mathcal{H}} = \sum_{p\in\mathcal{P}} \sum_{t\in\mathcal{T}}\sum_{h\in\mathcal{H}} \theta_{h,p,t} \tau_{t}\]

\(E_y^{\mathcal{H}}\): total carbon emissions of each technology in year \(y\)

\(\theta_{h,p,t}\): carbon emissions of technology \(h\) at location \(p\) in time step \(t\)

\(\tau_{t}\): duration of time step \(t\)

constraint_cost_capex_yearly()

Aggregates the capex of built capacity and of existing capacity.

\[A_{h,p,y} = f_h (\sum_{\tilde{y} = \max(y_0,y-\lceil\frac{l_h} {\mathrm{dy}}\rceil+1)}^y \alpha_{h,y}\Delta S_{h,p,\tilde{y}} + \sum_{\hat{y}=\psi(\min(y_0-1,y-\lceil\frac{l_h} {\mathrm{dy}}\rceil+1))}^{\psi(y_0)} \alpha_{h,y_0} \Delta s^\mathrm{ex}_{h,p,\hat{y}})\]

\(A_{h,p,y}\): annual capex of technology \(h\) at location \(p\) in year \(y\)

\(f_h\): annuity factor of technology \(h\)

\(\alpha_{h,y}\): unit cost of capital investment of technology \(h\) in year \(y\)

\(\Delta S_{h,p,y}\): size of built technology \(h\) (invested capacity after construction) at location \(p\) in year \(y\)

\(\Delta s^\mathrm{ex}_{h,p,y}\): size of the previously added capacities at location \(p\) in year \(y\)

\(l_h\): depreciation time of technology \(h\)

\(\mathrm{dy}\): interval between planning periods

constraint_cost_capex_yearly_total()

Sums over all technologies to calculate total capex.

\[CAPEX_y = \sum_{h\in\mathcal{H}}\sum_{p\in\mathcal{P}}A_{h,p,y} + \sum_{k\in\mathcal{K}}\sum_{n\in\mathcal{N}}A^\mathrm{e}_{k,n,y}\]

\(A_{h,p,y}\): annual capex of technology \(h\) at location \(p\) in year \(y\)

constraint_cost_opex_yearly()

Yearly opex for a technology at a location in each year.

\[OPEX_{h,p,y} = \sum_{t\in\mathcal{T}}\tau_t O_{h,p,t}^t + \gamma_{h,y} S_{h,p,y} + \gamma_{k,y}^\mathrm{e} S_{k,n,y}^\mathrm{e}\]

\(OPEX_{h,p,y}\): opex of operating technology \(h\) at location \(p\) in year \(y\)

\(\tau_t\): duration of time step \(t\)

\(O_{h,p,t}^t\): variable opex of operating technology \(h\) at location \(p\) in time step \(t\)

\(\gamma_{h,y}\): specific fixed opex of technology \(h\) in year \(y\)

\(S_{h,p,y}\): installed capacity of technology \(h\) at location \(p\) in year \(y\)

\(\gamma_{k,y}^\mathrm{e}\): specific fixed opex of storage technology \(k\) in year \(y\)

\(S_{k,n,y}^\mathrm{e}\): installed capacity of storage technology \(k\) at node \(n\) in year \(y\)

constraint_cost_opex_yearly_total()

Sums over all technologies to calculate total opex.

\[OPEX_y = \sum_{h\in\mathcal{H}}\sum_{p\in\mathcal{P}} OPEX_{h,p,y}\]

\(OPEX_{h,p,y}\): opex of operating technology \(h\) at location \(p\) in year \(y\)

constraint_technology_capacity_limit()

Limited capacity_limit of technology.

\[\text{if existing capacities < capacity limit: } s^\mathrm{max}_{h,p,y} \geq S_{h,p,y}\]

\[\text{else: } \Delta S_{h,p,y} = 0\]

\(S_{h,p,y}\): installed capacity of technology \(h\) at location \(p\) in year \(y\)

\(s^\mathrm{max}_{h,p,y}\): capacity limit of technology \(h\) at location \(p\) in year \(y\)

\(\Delta S_{h,p,y}\): size of built technology \(h\) (invested capacity after construction) at location \(p\) in year \(y\)

constraint_technology_construction_time()

Construction time of technology: time between investment and availability.

\[\text{if start time step in set time steps yearly: } \Delta S_{h,p,y} = \Delta S_{h,p,(y-dy^{\mathrm{construction}})}^\mathrm{invest}\]

\[\text{elif start time step in set time steps yearly entire horizon:} \Delta S_{h,p,y} = \Delta s^\mathrm{ex,invest}_{h,p,(y-dy^{\mathrm{construction}})}\]

\[\text{else: } \Delta S_{h,p,y} = 0\]

\(\Delta S_{h,p,y}\): size of built technology \(h\) (invested capacity after construction) at location \(p\) in year \(y\)

\(\Delta S_{h,p,y}^\mathrm{invest}\): size of invested technology at location \(p\) in year \(y\)

\(\Delta s^\mathrm{ex,invest}_{h,p,y}\): size of the previously invested capacities at location \(p\) in year \(y\)

constraint_technology_diffusion_limit()

Limits technology diffusion based on existing capacity in the previous year.

For storage and conversion technologies:

\[\Delta S_{k,n,y}\leq ((1+\vartheta_k)^{\mathrm{dy}}-1)(K_{k,n,y} + \omega \sum_{\tilde{n}\in\tilde{\mathcal{N}}}K_{k,\tilde{n},y}) +\mathrm{dy}(\xi\sum_{\tilde{k} \in\tilde{\mathcal{K}}}S_{\tilde{k},n,y} + \zeta_k)\]

For transport technologies:

\[\Delta S_{j,e,y}\leq ((1+\vartheta_j)^{\mathrm{dy}}-1)K_{j,e,y} + \mathrm{dy}(\xi\sum_{\tilde{j}\in\tilde{\mathcal{J}}} S_{\tilde{j},e,y} + \zeta_j)\]

\(\Delta S_{j,e,y}\): size of built technology \(j\) (invested capacity after construction) at location \(e\) in year \(y\)

\(\vartheta_j\): maximum diffusion rate of technology \(j\) which is the maximum increase in capacity between investment steps

\(K_{j,e,y}\): existing knowledge of how to install the technology \(j\) at location \(e\) in year \(y\)

\(\xi\): parameter which specifies the unbounded market share

\(\zeta_j\): parameter which specifies the unbounded capacity addition that can be added each year (only for delayed technology deployment)

\(dy\): interval between planning periods

\(\omega\): parameter which specifies the knowledge spillover rate

constraint_technology_lifetime()

Calculates remaining capacity of technologies based on the lifetime.

limited lifetime of the technologies. calculates ‘capacity’, i.e., the capacity at the end of the year and ‘capacity_previous’, i.e., the capacity at the beginning of the year.

\[S_{h,p,y} = \sum_{\tilde{y}=\max(y_0,y-\lceil\frac{l_h} {\Delta^\mathrm{y}}\rceil+1)}^y \Delta S_{h,p,\tilde{y}} + \sum_{\hat{y}=\psi(\min(y_0-1,y-\lceil\frac{l_h} {\Delta^\mathrm{y}}\rceil+1))}^{\psi(y_0)} \Delta s^\mathrm{ex}_{h,p,\hat{y}}\]

\(S_{h,p,y}\): installed capacity of technology \(h\) at location \(p\) in year \(y\)

\(\Delta S_{h,p,y}\): size of built technology \(h\) (invested capacity after construction) at location \(p\) in year \(y\)

\(\Delta s^\mathrm{ex}_{h,p,y}\): size of the previously invested capacities at location \(p\) in year \(y\)

constraint_technology_max_capacity_addition()

Max capacity addition of technology.

\[s^\mathrm{max}_{h} g_{i,p,y} \ge \Delta S_{h,p,y}\]

\(s^\mathrm{add, max}_{h}\): maximum capacity addition of technology \(h\)

\(g_{i,p,y}\): binary variable which equals 1 if technology is installed at location \(p\) in year \(y\)

\(\Delta S_{h,p,y}\): size of built technology \(h\) (invested capacity after construction) at location \(p\) in year \(y\)

constraint_technology_min_capacity_addition()

Min capacity addition of technology.

\[\Delta s^\mathrm{min}_{h} g_{i,p,y} \le \Delta S_{h,p,y}\]

\(\Delta s^\mathrm{min}_{h}\): minimum capacity addition of technology \(h\)

\(g_{i,p,y}\): binary variable which equals 1 if technology is installed at location \(p\) in year \(y\)

\(\Delta S_{h,p,y}\): size of built technology \(h\) (invested capacity after construction) at location \(p\) in year \(y\)

constraint_technology_on_off()

If technology is on, the binary variable is 1, else 0.

The min load constraint is expressed as six constraints (here for conversion technologies):

\[ \begin{align}\begin{aligned}m^\mathrm{min}_{i,n,t}S^\mathrm{approx}_{i,n,t}\leq G^\mathrm{r}_{i,n,t} \leq S^\mathrm{approx}_{i,n,t}\\0 \leq S^\mathrm{approx}_{i,n,t} \leq s^\mathrm{max}_{i,n,y} B_{i,n,t}\\S_{i,n,y} - s^\mathrm{max}_{i,n,y}(1-B_{i,n,t}) \leq S^\mathrm{approx}_{i,n,t} \leq S_{i,n,y}\end{aligned}\end{align} \]

\(m^\mathrm{min}_{i,n,t}\): minimum load parameter for technology \(i\), node \(n\), time step \(t\)

\(G_{i,n,t}^\mathrm{r}\): reference carrier flow of the technology \(i\) at node \(n\) in time step \(t\)

\(S_{h,p,y}\): installed capacity of technology \(h\) at location \(p\) in year \(y\)

\(B_{i,n,t}\): binary variable indicating whether the technology is on or off for technology \(i\), node \(n\), time step \(t\)

\(S^\mathrm{approx}_{i,n,t}\): helper variable that represents the product of \(S_{i,n,y}\) and \(B_{i,n,t}\)

\(s^\mathrm{max}_{i,n,y}\): Big-M limit on \(S_{h,p,y}\)