# Monte Carlo Co-Simulations¶

This tutorial will walk through how to set up a HELICS Monte Carlo simulation using two techniques: (1) in series on a single machine, and (2) in parallel on an HPC cluster using Merlin. We assume that you have already completed the orchestration tutorial with Merlin and have some familiarity with how Merlin works.

## Where is the code?¶

Code for the Monte Carlo simulation and the full Merlin spec and be found in the HELICS Examples Repo. If you have issues navigating the examples, visit the HELICS Gitter page or the user forum on GitHub.

The necessary files are:

## What is this co-simulation doing?¶

This example walks through how to set up a probabilistic model with Monte Carlo simulations. This Monte Carlo co-simulation is built from a simple two federate example, based on the Endpoint Federates Example. In this example, there is a Charger federate which publishes voltage and a Battery federate which publishes current.

All of the HELICS configurations are the same as in the Endpoint example. The internal logic of the federates has been changed for this implementation. The Charger federate assumes the role of deciding if the Battery should continue to charge. The Battery sends a message of its current SOC (state of charge), a number between 0 and 1. If the SOC is less than 0.9, the Battery is instructed to continue charging, otherwise, it is instructed to cease charging. The Battery federate has all the logic internal for adding energy and selecting a new “battery” (charging rate) if the SOC is deemed sufficient. Energy is added to the “battery” according to the previous time interval and the charge rate of the battery. In this way, the only stochastic component to the system is the selected charge rate. For example, the Endpoint Example allowed the Battery federate to randomly select batteries of different sizes, and the Charger to select charge rates from a list of options. In this implementation, the battery size (capacity in kWh) is constant.

This simplification allows us to isolate a single source of uncertainty: the charge rate.

The co-simulation relies on stochastic sampling of distributions – an initial selection of vehicles for the EV charging garage. We want to ensure that we are not overly reliant on any one iteration of the co-simulation. To manage this, we can run the co-simulation N times, or a Monte Carlo co-simulation. The result will be a posterior distribution of the instantaneous power draw over a desired period of time.

## Probabilistic Uncertainty Estimation¶

A Monte Carlo simulation allows a researcher to sample random numbers repeatedly from a predefined distribution to explore and quantify uncertainty in their analysis. Additional detail about Monte Carlo methods can be found on Wikipedia and MIT Open Courses.

In a Monte Carlo co-simulation, a probability distribution of possible values can be used in the place of any static value in any of the simulators. For example, a co-simulation may include a simulator (federate) which measures the voltage across a distribution transformer. We can quantify measurement error by replacing the deterministic (static) value of the measurement with a random value from a uniform distribution. Probabilistic distributions are typically described with the following notation:

M ~ U(a,b)

Where M is the measured voltage, a is the lower bound for possible values, and b is the upper bound for possible values. This is read as, “M is distributed uniformly with bounds a and b.”

The uniform distribution is among the most simple of probability distributions. Additional resources on probability and statistics are plentiful; Statistical Rethinking is highly recommended.

### Monte Carlo Co-sim Example: EV Garage Charging¶

The example co-simulation to demonstrate Monte Carlo distribution sampling is that of an electric vehicle (EV) charging garage. Imagine a parking garage that only serves EVs, has a static number of charging ports, and always has an EV connected to a charging port. An electrical engineer planning to upgrade the distribution transformer prior to building the garage may ask the question: What is the likely power draw that EVs will demand?

#### Probability Distributions¶

Likely is synonymous for probability. As we are interested in a probability, we cannot rely on a deterministic framework for modeling the power draw from EVs. I.e., we cannot assume that we know a priori the exact demand for Level 1, Level 2, and Level 3 chargers in the garage. A deterministic assumption would be equivalent to stating, e.g., that 30% of customers will need Level 1 charge ports, 50% will need Level 2, and 20% will need Level 3. What if, instead of static proportions, we assign a distribution to the need for each level of charge port. The number of each level port is discrete (there can’t be 0.23 charge ports), and we want the number to be positive (no negative charge ports), so we will use the Poisson distribution. The Poisson distribution is a function of the anticipated average of the value λ and the number of samples k. Then we can write the distribution for the number of chargers in each level, L, as

L ~ P(k,λ)

Let’s extend our original assumption that the distribution of chargers is static to Poisson distributed, and let’s assume that there are 100 total charging ports:

L1 ~ P(100,0.3)

L2 ~ P(100,0.5)

L3 ~ P(100,0.2)

What if we weren’t entirely certain that the average values for L1, L2, L3 are 0.3, 0.5, 0.2, we can also sample the averages from a normal distribution centered on these values with reasonable standard deviations. We can say that:

λ ~ N(μ,σ)

Which means that the input to L is distributed normally with average μ and standard deviation σ.

Our final distribution for modeling the anticipated need for each level of charging port in our k = 100 EV garage can be written as:

L ~ P(k,λ)

λ ~ N(μ,σ)

L1

L2

L3

μ

0.3

0.5

0.2

σ

~ N(1,3)

~ N(1,2)

~ N(0.05,0.25)

Notice that the individual overplotted distributions in the two histograms above are different – there is more flexibility encoded into the second. The distributions in the second plot describe the following assumptions about the anticipated need for Level 1, 2, and 3 chargers:

1. The number of charging ports is discrete and positive (Poisson).

2. The variance in the number of ports should be normally distributed.

3. The average percentage of Level 1, 2, and 3 chargers is 30%, 50%, and 20%, respectively.

4. The variance around the average is uniformly distributed.

5. The variance is relatively very broad for Level 1, broad for Level 2, and very constrained for Level 3. This means we are very confident in our guess of the average percentage for Level 3 chargers, less confident for Level 2, and much less confident for Level 3.

We have described the individual distributions for each level of charging port. What we don’t know, prior to running the Monte Carlo co-simulation, is how these distributions will jointly impact the research question.

#### Research Question Configuration¶

We want to address the research question: What is the likely power draw that EVs will demand?

At the beginning of the co-simulation, the distributions defined above will be sampled N times within the EV federate, where N = the number of parking spots/charging ports in the garage. The output of the initial sampling is the number of requested Level 1, 2, and 3 charging ports. The SOC for the batteries on board are initialized to a uniform random number between 0.05 and 0.5, and these SOC are sent to the Charger federate. If the SOC of an EV battery is less than 0.9, the EV Controller federate tells the EV battery in the EV federate to continue charging. Otherwise, the EV Charger disconnects the EV battery, and instructs the it to sample a new EV battery from the distributions (one sample).

After the two federates pass information between each other – EV Battery sends SOC, EV Charger instructs whether to keep charging or resample the distributions – the EV Battery calculates the total power demanded in the last time interval.

## Execution and Results¶

Execution can be done with either a simple script (provided on the repo), or with Merlin.

### Manual Orchestration Execution¶

Manual implementation of the co-simulation is done with the helper script advanced_orchestration.py, with command line execution:

$python advanced_orchestration.py  This implementation will run a default co-simulation. The default parameters are: samples = 30 output_path = os.getcwd() numEVs = 10 hours = 24 plot = 0 run = 1  This means that we are generating 30 JSON files with unique seeds, we are using the current operating directory as the head for the output path, we are simulating 10 EVs in the co-simulation for one day, we are not running individual plots for each simulation, and we are executing the JSON files with helics_cli after they have been created. If we wanted to run a Monte Carlo co-sim with different parameters, this would be: $ python advanced_orchestration.py 10 . 100 24*7 0 0


This execution would create 10 JSON files with unique seeds, set the current directory as the head for the output path, simulate 100 EVs for a week, not generate plots with each simulation, and not execute the JSON files with helics_cli (meaning that helics_cli will not be called automatically – the user will need to manually execute helics_cli for each JSON file).

You may decide to adapt advanced_orchestration.py to suite your needs within the Merlin environment, in which case you would only need the helper script to create the JSON files. If you elect to execute helics_cli for the generated runner JSON files using the helper script, subdirectories are created for the helics_cli runner JSON files and for the csv results. Results for the default simulation are in the repo and can be used for confirming accurate execution.

out_json = output_path + "/cli_runner_scripts"
out_data = output_path + "/results"


In the runner scripts directory, there will be 30 JSON files. Each will have a unique seed parameter, otherwise they will all look identical:

{
"federates": [
{
"exec": "helics_broker --federates=2 --loglevel=data --coretype=tcpss --port 12345",
"host": "localhost",
"loglevel": "data",
"name": "broker_0"
},
{
"exec": "python3 Battery.py --port 12345 --seed 10 --numEVs 10 --hours 24 --plot 0 --outdir [path to local HELICS-Examples/user_guide_examples/advanced/advanced_orchestration dir]/results",
"host": "localhost",
"loglevel": "data",
"name": "Battery_0"
},
{
"exec": "python3 Charger.py --port 12345 --numEVs 10 --hours 24",
"host": "localhost",
"loglevel": "data",
"name": "Charger_0"
}
],
}


The final result of the default Monte Carlo co-simulation is shown below.

This is a time series density plot. Each simulation is a green line, and the blue solid line is the median of all simulations. From this plot, we can see that (after the system initializes, after a few hours) the maximum demand from EVs in the garage will be roughly 125 kW. We could improve the analysis by conducting an initialization step and by running the simulation for a longer time period. This type of analysis provides the engineer with information about the probability that demand for power from N EVs will be X kW. The most commonly demanded power is less than 50 kW – does the engineer want to size the power conduit to provide median power, or maximum power?

### Merlin Orchestration Execution¶

In this specification we will be using the helics_cli to execute each co-simulation run since this is a Monte Carlo simulation. This means that helics_cli will be executed multiple times with different helics_cli runner files.

#### Co-simulation Reproduction¶

Management of multiple iterations of the co-simulation can be done by setting the seed as a function of the number of brokers, where there will be one broker for each iteration. In Python 3.X:

import argparse

parser = argparse.ArgumentParser(description="EV simulator")
"--seed",
type=int,
default=0,
help="The seed that will be used for our random distribution",
)
parser.add_argument("--port", type=int, default=-1, help="port of the HELICS broker")

args = parser.parse_args()
np.random.seed(args.seed)


#### helics_cli in Merlin¶

Since we are using the helics_cli to manage and execute all the federates, we need to create these runner files for helics_cli. There is a provided python script called make_samples_merlin.py (see the simple subfolder in the code for the example) that will generate the runner file and a csv file that will be used in the study step. helics_cli will start each of these federates. In the Merlin spec, Merlin will be instructed to execute the helics_cli with all the generated helics_cli runner files.

#### Merlin Specification¶

##### Environment¶

In the Merlin spec we will instruct Merlin to execute N number of the Monte Carlo co-simulations. The number of samples is the number specified as the N_SAMPLES env variable in the env section of the Merlin spec.

env:
variables:
OUTPUT_PATH: ./UQ_EV_Study
N_SAMPLES: 10


We set the output directory to UQ_EV_Study, this is where all the output files will be stored. Every co-simulation run executed by Merlin will have its own subdirectory in ./UQ_EV_Study.

##### Merlin Step¶

Remember this step is for Merlin to setup all the files and data it needs to execute its jobs. In the Monte Carlo co-simulation there is a python script we created that will generated the helics_cli runner files that Merlin will use when it executes the helics_cli. The make_samples_merlin.py script (located under the simple subfolder of the advanced orchestration example code) will also output a csv file that Merlin will use. The csv file contains all the names of the runner files. Merlin will go down this list of file names and execute the helics_cli for each file name.

merlin:
samples:
generate:
cmd: |
python3 $(SPECROOT)/simple/make_samples_merlin.py$(N_SAMPLES) $(MERLIN_INFO) cp$(SPECROOT)/Battery.py $(MERLIN_INFO) cp$(SPECROOT)/Charger.py $(MERLIN_INFO) file:$(MERLIN_INFO)/samples.csv
column_labels: [FED]


The samples the get generated should look something like below. This is the runner file that helics_cli will use to start the co-simulation.

{
"federates": [
{
"directory": ".",
"exec": "helics_broker --federates=2 --loglevel=5 --type=tcpss --port 12345",
"host": "broker",
"name": "broker_0",
"loglevel": 3
},
{
"directory": ".",
"exec": "python3 Battery.py --port 12345 --seed 1",
"host": "broker",
"name": "Battery",
"loglevel": 3
},
{
"directory": ".",
"exec": "python3 Charger.py --port 12345",
"host": "broker",
"name": "Charger",
"loglevel": 3
}
],
"name": "Generated by make samples"
}


Once the samples have been created, we copy the 2 federates to the MERLIN_INFO directory.

##### Study Step¶

We have made it to the study step. This step will execute all 10 Monte Carlo co-simulations. There are 2 steps in the study step. The first step is the start_parallel_sims step. This step will use the helics_cli to execute each co-simulation. The second step, cleanup depends on the first step. Once start_parallel_sims is complete the cleanup step will remove any temporary data that is no longer needed.

study:
- name: start_parallel_sims
description: Run a bunch of UQ sims in parallel
run:
cmd: |
helics run --path=$(MERLIN_INFO)/$(FED)
echo "DONE"
- name: cleanup
description: Clean up
run:
cmd: rm \$(MERLIN_INFO)/samples.csv
depends: [start_parallel_sims_*]


Below is what the DAG of the Merlin study will look like. Each of the Co-Sim_n bubbles represents the Monte Carlo simulation. Each co-sim runs in parallel with each other since there is no dependency on the output that each co-sim runs.

## Questions and Help¶

Do you have questions about HELICS or need help?

1. Come to office hours!

2. Post on the gitter!

3. Place your question on the github forum!