# Multi-Agent Reinforcement Learning for Active Voltage Control on Power Distribution Networks (MAPDN)

This is the implementation of the paper Multi-Agent Reinforcement Learning for Active Voltage Control on Power Distribution Networks.

MAPDN is an environment of distributed/decentralised active voltage control on power distribution networks and a batch of state-of-the-art multi-agent actor-critic algorithms that can be used for training.

The environment implementation follows the multi-agent environment framework provided in PyMARL. Therefore, all baselines that are compatible with that framework can be easily applied to this environment.

## Summary of the Repository

This repository includes the following components.

• An environment of active voltage control (decentralised and distributed);

• A training framework for MARL;

• 10 MARL algorithms;

• 5 voltage barrier functions;

• Bowl, L1, L2, Courant Beltrami, and Bump.
• Implementation of droop control and OPF in Matlab.

## A Brief Introduction of the Task

In this section, we give a brief introduction of this task so that the users can easily understand the objective of this environment.

Objective: Each agent controls a PV inverter that generates the reactive power so that the voltage of each bus is varied and within the safety range defined as $0.95 \ p.u. \leq v_{k} \leq 1.05 \ p.u., \ \forall k \in V$, where $V$ is the set of buses of the whole system and $p.u.$ is a unit to measure voltage. Since each agent’s decision could influence each other due to property of power networks and not all buses is installed a PV, agents should cooperate to control the voltage of all buses in a power network. Also, each agent can only observe the partial information as the observation. This problem is natually a Dec-POMDP.

Action: The reactive power is constrained by the capacity of the equipment, and the capacity is related to the active power of PV. As a result, the range of reactive power is dynamically varied. Mathematically, the reactive power of each PV inverter is represented as $$q_{k}^{\scriptscriptstyle PV} = a_{k} \ \sqrt{(s_{k}^{\scriptscriptstyle \max})^{2} – (p_{k}^{\scriptscriptstyle PV})^{2}},$$ where $s_{k}^{\scriptscriptstyle \max}$ is the maximum apparent power of the $k\text{th}$ node that is dependent on the physical capacity of the PV inverter; $p_{k}^{\scriptscriptstyle PV}$ is the instantaneous PV active power. The action we control is the variable $0 \leq a_{k} \leq 1$, indicating the percentage of the intantaneous capacity of reactive power. For this reason, the action is continuous in this task.

Observation: Each agent can observe the information of the zone where it belongs. For example, in Figure 1 the agent on bus 25 can observe the information in zone 3. Each agent’s observation consists of the following variables within the zone:

• PV Active Power,
• PV Reactive Power,
• Voltage.

Figure 1: Illustration on the 33-bus network. Each bus is indexed by a circle with a number. Four control regions are partitioned by the smallest path from the terminal to the main branch (bus 1-6). We control the voltage on bus 2-33 whereas bus 0-1 represent the substation with constant voltage and infinite active and reactive power capacity. G represents an external generator; small Ls represent loads; and emoji of sun represents the location where a PV is installed.

Reward: The reward function is shown as follows:
$$\mathit{r} = – \frac{1}{|V|} \sum_{i \in V} l_{v}(v_{i}) – \alpha \cdot l_{q}(\mathbf{q}^{\scriptscriptstyle PV}),$$
where $l_{v}(\cdot)$ is a voltage barrier function that measures whether the voltage of a bus is within the safety range; $l_{q}(\mathbf{q}^{\scriptscriptstyle PV})=\frac{1}{|\mathcal{I}|}||\mathbf{q}^{\scriptscriptstyle PV}||_{1}$ that can be seen as a simple approximation of power loss, where $\mathbf{q}^{\scriptscriptstyle PV}$ is a vector of agents’ reactive power, $\mathcal{I}$ is a set of agents and $\alpha$ is a multiplier to adjust the balance between voltage control and the generation of reactive power. In this work, we investigate different forms of $l_{v}(\cdot)$. Literally, the aim of this reward function is controlling the voltage, meanwhile minimising the power loss that is correlated with the economic loss.

## Installation of the Dependencies

1. Install Anaconda.
2. After cloning or downloading this repository, assure that the current directory is [your own parent path]/MAPDN.
3. Execute the following command.

conda env create -f environment.yml
4. Activate the installed virtual environment using the following command.

conda activate mapdn

2. Unzip the zip file and you can see the following 3 folders:

• case33_3min_final
• case141_3min_final
• case322_3min_final
3. Go to the directory [Your own parent path]/MAPDN/environments/var_voltage_control/ and create a folder called data.

4. Move the 3 extracted folders by step 2 to the directory [Your own parent path]/MAPDN/environments/var_voltage_control/data/.

### Background

There are 2 modes of tasks included in this environment, i.e. distributed active voltage control and decentralised active voltage control. Distributed active voltage control is the task introduced in the paper Multi-Agent Reinforcement Learning for Active Voltage Control on Power Distribution Networks, whereas Decentralised active voltage control is the task that most of the prior works considered. The primary difference between these 2 modes of tasks are that in decentralised active voltage control the equipments in each zone are controlled by an agent, while in distributed active voltage control each equipment is controlled by an agent (see Figure 1).

### How to use?

If you would attempt distributed active voltage control, you can set the argument for train.py and test.py as follows.

python train.py --mode distributed

python test.py --mode distributed

If you would attempt decentralised active voltage control, you can set the argument for train.py and test.py as follows.

python train.py --mode decentralised

python test.py --mode decentralised

## Quick Start

You can execute the following command to train a model on a power system using the following command.

python train.py --alg matd3 --alias 0 --mode distributed --scenario case33_3min_final --voltage-barrier-type l1 --save-path trial


The the meanings of the arguments are illustrated as follows:

• --alg indicates the MARL algorithm you would like to use.
• --alias is the alias to distinguish different experiments.
• --mode is the mode of the envrionment. It contains 2 modes, e.g. distributed and decentralised. Distributed mode is the one introduced in this work, whereas decentralised mode is the traditional environment used by the prior works.
• --scenario indicates the power system on which you would like to train.
• --voltage-barrier-type indicates the voltage barrier function you would like to use for training.
• --save-path is the path you would like to save the model, tensorboard and configures.

After training, you can exclusively test your model to do the further analysis using the following command.

python test.py --save-path trial/model_save --alg matd3 --alias 0 --scenario case33_3min_final --voltage-barrier-type l1 --test-mode single --test-day 730 --render


The the meanings of the arguments are illustrated as follows:

• --alg indicates the MARL algorithm you used.
• --alias is the alias you used to distinguish different experiments.
• --mode is the mode of the envrionment you used to train your model.
• --scenario indicates the power system on which you trained your model.
• --voltage-barrier-type indicates the voltage barrier function you used for training.
• --save-path is the path you saved your model. You just need to give the parent path including the directory model_save.
• --test-mode is the test mode you would like to use. There are 2 modes you can use, i.e. single and batch.
• --test-day is the day that you would like to do the test. Note that it is only activated if the --test-mode is single.
• --render indicates activating the rendering of the environment.

## Interaction with Environment

The simple use of the environment is shown as the following codes.

state, global_state = env.reset()

for t in range(240):
actions = agents.get_actions() # a vector involving all agents' actions
reward, done, info = env.step(actions)

## Reproduce the Results in the Paper

Users can easily reproduce the results shown in the paper by running the bash script provided with the default configures provided in this repository, e.g.,

source train_case33.sh 0 l1 reproduction

source train_case33.sh 0 l2 reproduction

source train_case33.sh 0 bowl reproduction

source train_case141.sh 0 l1 reproduction

source train_case141.sh 0 l2 reproduction

source train_case141.sh 0 bowl reproduction

source train_case322.sh 0 l1 reproduction

source train_case322.sh 0 l2 reproduction

source train_case322.sh 0 bowl reproduction

The arguements of the above bash scripts are as follows.

$1: --alias$2: --voltage-loss-type
$3: --save-path Note: these training scripts are based on the assumption that you have at least 2 GPUs with 12 GB memory. If the above conditions do not satisfy your own local situation, please manually modify the allocation of GPUs. The results in the paper are produced by Geforce RTX 2080Ti. ## Brief Introduction of Scenarios We show the basic settings of all scenarios provided in this repository. Scenario No. Loads No. Regions No. PVs (Agents)$p_{\text{max}}^{\scriptscriptstyle{L}}p_{\text{max}}^{\scriptscriptstyle{PV}}\$
Case33 32 4 6 3.5 MW 8.75 MW
Case141 84 9 22 20 MW 80 MW
Case322 337 22 38 1.5 MW 3.75 MW

2. Extract the case files and move them to the directory [Your own parent path]/MAPDN/traditional_control.

### Running

• Reproduce the results for droop control by running the file pf_droop_matpower_all.m.

• Reproduce the results for OPF by running the file opf_matpower_all.m.

See the annotation in the files for more details.

## API Usage

For more details of this environment, users can check the upcoming API Docs.

## Citation

If you would use this environment or part of this work, please cite the following paper.

@misc{wang2021multiagent,
title={Multi-Agent Reinforcement Learning for Active Voltage Control on Power Distribution Networks},
author={Jianhong Wang and Wangkun Xu and Yunjie Gu and Wenbin Song and Tim C. Green},
year={2021},
eprint={2110.14300},
archivePrefix={arXiv},
primaryClass={cs.LG}
}


## Contact

If you have any issues or any intention of cooperation, please feel free to contact me via [email protected].

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