Power Grid Investment Module - user guide

Contents:

• Modelling documentation
• Examples
• What it does
• Running an optimisation
• Input data
  • Grid data
  • Time sample
  • Parameters
• Analysis of results
• More about optimisation model

Modelling documentation

A separate (draft) document provides more details about the modelling framework and the theoretical context of the PowerGIM model. This is available here.

Examples

For a quick demonstration of how PowerGIM works, have a look at these Jupyter notebooks:

1. Example of deterministic optimisation
2. Example with added stochastic parameters

What it does

PowerGIM is a module for grid investment analyses that is included with the PowerGAMA python package. It is a power system expansion planning model that can consider both transmission and generator investments.

PowerGIM works by finding the optimal investments amongst a set of specified candidates such that the net present value of total system costs (capex and opex) are minimised.

It is built on top of the Pyomo/PySP package.

Two-stage optimisation

PowerGIM is formulated as a two-stage optimisation problem, and there may be a time delay between the two investment stages. First-stage variables represent the here-and-now investments that are of primary interest. Second-stage variables include operational decisions and second-stage investments.

Uncertainty - stochastic programming

For many investment decisions it is important to consider uncertainties and identify solutions that are good for all likely values of the uncertain parameters. In the context of grid planning, relevant uncertainties are for example future generator capacity and energy demand at different grid locations, power prices. These things may have a huge impact on the benefit of different investments alternatives.

Rather than just finding the optimal solution for a specific set of assumptions, it is more relevant to find the solution that is best for the whole range of potential realisations of the uncertain parameters. This is stochastic programming.

PowerGIM includes this capability via the two-stage formulation. Uncertain parametes and their potential values are specified via a scenario tree.

First stage variables (here-and-now decisions) are made without knowing which scenario is realised, while second stage variables are different for the different scenarios.

A simple example of a two-stage stochastic optimisation problem with three scenarios (representing uncertainty about future wind farm capacities) and their probabilities (P) is shown below:

Running an optimisation

See the examples.

The general steps when using PowerGIM in a Python script/notebook to specify and solve optimisation problems are:

Preparations:

1. Create input data sets (csv and xml)
   • these specify existing infrastructure and candidate investments

Script:

2. Read input data and create optimisation model
3. Create model instance
   • for stochastic problem: specify scenario tree and model instance creation call-back function
4. Solve model
5. Save/inspect/analyse results

Input data

Grid data

Grid data is imported from CSV files in almost the same format as for PowerGAMA. There are files for nodes, branches, generators and consumers.

Nodes

Node data are specified in a CSV file with one element per row, with columns as shown below:

Branches

Branch data are specified in a CSV file with one element per row, with columns as shown below:

Branches have from and to references that must match a node identifier in the list of nodes. * expand/expand2 is 0 if no expansion should be considered (not part of optimisaion) * distance may be left blank. Then distance is computed as the shortest distance between the associated nodes (based on lat/lon coordinates) * capacity2 is already decided additional branch capacity that will be added at stage two (optional input).

Generators

Generator data are specified in a CSV file with one element per row, with columns as shown below:

• The average power constraint (pavg) is used to represent generators with large storage. pavg=0 means no constraint on average output is used (no storage constraint).
• pmax2 is already decided increase in generator capacity in stage 2

Consumers

Consumer (power demand) data are specified in a CSV file with one element per row, with columns as shown below:

• There may be any number of consumers per node, although zero or one is typical.
• demand_avg gives the average demand, which is easily computed from the annual demand if necessary.
• demand_ref gives the name of the demand profile (time sample) which gives the variation over time. Demand profiles should be normalised and have an annual average of 1.

Time sample

A set of time series or samples are used to represent the variability in renewable energy availability, power demand and generator fuel costs (power prices).

These data are provided as a CSV file with one profile/sample per column, with the column header being the profile string identifier, and one row per timestamp.

the time samples are used together with base values to get demand, available power and fuel costs at a given time as follows:

demand(t) = demand_avg × demand_ref(t) fuelcost(t) = fuelcost × fuelcost_ref(t) pmax(t) = (pmax+pmax2) × inflow_fac × inflow_ref(t)

Parameters

Investment costs and other parameters are provided in an XML file with the following structure:

<?xml version="1.0" encoding="utf-8"?>
<powergim>
<nodetype>
  <item name="ac" L="1" S="50e6" />
  <item name="dc" L="1" S="1" />
</nodetype>
<branchtype>
  <item name="ac"      B="5000e3" Bdp="1.15e3"  Bd="656e3"  CL="1562e3"  CLp="0"        CS="4813e3"  CSp="0"        maxCap="400"  lossFix="0"     lossSlope="5e-5" />
  <item name="dcmesh"   B="5000e3" Bdp="0.47e3"  Bd="680e3"  CL="0"       CLp="0"        CS="0"       CSp="0"        maxCap="2000" lossFix="0"     lossSlope="3e-5" />
  <item name="dcdirect" B="5000e3" Bdp="0.47e3"  Bd="680e3"  CL="20280e3" CLp="118.28e3" CS="129930e3" CSp="757.84e3" maxCap="2000" lossFix="0.032" lossSlope="3e-5" />
  <item name="conv"     B="0"      Bdp="0"       Bd="0"      CL="10140e3" CLp="59.14e3"  CS="64965e3" CSp="378.92e3" maxCap="2000" lossFix="0.016" lossSlope="0" />
  <item name="ac_ohl"   B="0"      Bdp="0.394e3" Bd="1187e3" CL="1562e3"  CLp="0"        CS="0"       CSp="0"        maxCap="4000" lossFix="0"     lossSlope="3e-5" />
</branchtype>
<gentype>
  <item name="alt"  CX="10" CO2="0" />
  <item name="wind" CX="0"  CO2="0" />
</gentype>

<parameters
  financeInterestrate="0.05"
  financeYears="30"
  omRate="0.02"
  curtailmentCost="0"
  CO2price="0"
  VOLL="0"
  stage2TimeDelta="1"
  stages="2"
/>
</powergim>

Most of the parametes in the nodetype, branchtype and gentype blocks are cost parameters branchtype has the following additional parameters related to power losses, and the maximum allowable power rating per cable system (maxCap)

Parameters specified in the parameters block are:

• financeInterestrate = discount rate used in net present value calculation of generation costs and operation and maintenance costs
• financeYears = financial lifetime of investments - the period over which the total costs are computed (years)
• omRate = fraction specifying the annual operation and maintenance costs relative to the investment cost
• curtailmentCost = penalty cost for curtailment of renewable energy (EUR/MWh)
• CO2price = costs for CO2 emissions (EUR/kgCO2)
• VOLL = penalty cost for load shedding (demand not supplied) (EUR/MWh)
• stage2TimeDelta = time duration between investment stage 1 and 2 (years)
• stages = number of investment stages (2 is the only choice at the moment)

Analysis of results

There are some different ways to analyse the optimisation results:

• save to CSV file and analyse with tool of choice
• plot on map (candidate investments / stage 1 result / stage 2 results), using powergim.SipModel.extractResultingGridData(...) and powergama.plots.plotMap(...)
• inspect variables directly using Pyomo functionality (pyomo is the python package used to formulate the optimisation problem)

More about the PowerGIM optimisation model

Cost model

Investment cost

Branches, Nodes and generators:

• cost_b = B + Bbd ⋅ b ⋅ d + Bd ⋅ d + Σ(Cp ⋅ p + C)
  • The sum is over the two branch endpoints, that may be on land or at sea.
  • d = branch distance (km)
  • p = power rating (MW)
  • B = fixed cost (EUR)
  • Bdp = cost dependence on both distance and rating (EUR/km/MW)
  • Bd = cost dependence on distance (EUR/km)
  • C = fixed endpoint cost (CL=on land, CS=at sea) (EUR)
  • Cp = endpoint cost dependence on rating (EUR/MW)
• cost_n = N
  • N = fixed cost (NL=on land, NS=at sea)
• cost_g = Gp ⋅ capacity
  • Gp = generator cost per power rating (EUR/MW)

Present value vs future value(s) - Present value factor (pv) for translating future value to present value, and annuity factor (a) for translating future cash flow to present value:

• pv(r,T0) = 1/(1+r)^T0
• a(r,T) = 1/r ⋅ [1 - 1/(1+r)^T]
  • T0 = year of investment (0 for stage 1)
  • T = number of periods (years) (financeYears)
  • r = discount rate (financeInterestrate)

Operation and maintenance (O&M) and salvage factors:

• om_factor = omRate ⋅ [a(r,T1)-a(r,T0)]
  • omRate = annual O&M cost as fraction of investment cost
• salvage_factor = T0/T(1/(1+r)^(T-T0))
  • salvage value is the remaining value after the financial lifetime (non-zero for investments in stage 2, since they have more life left than stage 1 investments)

Present value of investments including O&M costs and salvage value:

pv_cost_inv = Σcost ⋅ pv ⋅ (1 + om_factor - salvage_factor)

The sum is over all investments

Operational cost

Costs per year are:

cost_op = sum over time sample { Pg ⋅ (fuelcost + emissionrate ⋅ CO2price) + Pshed ⋅ VOLL } ⋅ samplefactor

• Pg = generator output (MW)
• fuelcost = generator cost (EUR/MWh), including time profile
• emissionrate = CO2 emissions per power output (kgCO2/MWh)
• CO2price = CO2 tax
• Pshed = load shed (MW)
• VOLL = value of lost load (load shedding cost) (EUR/MWh)
• samplefactor = number of hours represented by value in time sample (hours)

Present value of generation costs:

pv_cost_op = Σ cost_op ⋅ a

The sum is over all generators.

Total costs

Total costs that is the objective function in the optimisation problem:

cost = pv_cost_inv + pv_cost_op

Power losses

power out = power in (lossFix + lossSlope*d)

• lossFix = loss factor, fixed part
• lossSlope = loss factor dependence on branch distance (1/km)

Variables

These are the optimisation problem variables

• branchNewCapacity = capacity of new branches
• branchNewCables = number of new cables (integer)
• newNodes = number of new nodes (integer)
• genNewCapacity = new generation capacity
• branchFlow12 = power flow on branch in positive direction
• branchFlow21 = power flow on branch in negative direction
• generation = generator output
• loadShed = load shedding

Constraints

Constraints are included for

1. Branch power flow is limited by branch capacity (in both directions)
2. New branch capacity requires new branches
3. A node is required at each branch endpoint
4. Generator output is limited by capacity and energy availability
5. Generator output average over entire time sample is limited by average power available (energy limitation for storage generators)
6. CO2 emissions are limited by emission cap
7. Power balance at each node (branch power loss is included here)