Data Study on Electric Vehicles
The skills the author demoed here can be learned through taking Data Science with Machine Learning bootcamp with NYC Data Science Academy.
Contributed by Wann-Jiun Ma. He is currently attending the NYC Data Science Academy Online Data Science Bootcamp program. This post is based on his second class project - Data Analysis and Visualization with Shiny.
Introduction
As data shows electric vehicles (EVs) will be widespread in coming future, it is interesting to examine the impact of large-scale integration of EVs on power grids. The owners of EVs need to charge their vehicles on a daily basis to ensure that there is enough power when they drive to work, which may introduce a huge electricity demand to the power distribution company.
It is interesting to see what may happen to power grids if there are millions of people charging their EVs during the same time period. If power plants cannot provide enough electricity to meet the demand of so many EVs at the same time, can people schedule their EVs in a way so that power plants won't reach capacity limitations? One main concern when people consider buying EV is to save fuel cost. But do we need to pay more for charging an EV? Can we design a charging strategy to save charging cost? There are so many interesting questions to answer. Let's start our analysis!
Data Analysis and Visualization with Shiny
First, we summarize the locations of the charging stations in the States to have a big picture. The data is downloaded from Open Charge Map https://openchargemap.org/site. Open Charge Map provides an API for users to consume and contribute data. We use the API provided by Open Charge Map to retrieve charging location information. We agree with the license term listed at https://openchargemap.org/site/develop#api. The data format is JSON and we parse the data to extract location information including latitude, longitude, address, etc. After data wrangling, we store the information in CSV format for later use. All codes can be found at https://github.com/Wann-Jiun/nycdsa_project_2_shiny.
The interactive map is built by leaflet. The map will group charging stations based on their locations. If we want to find the address of a charging station, we can just zoom in on the map to locate a particular charging station. Within renderLeaflet, we also plot the numbers of stations in major cities.
It looks like the number of charging stations in LA is about twice more than that in NYC! Austin (TX) has more charging stations than NYC! For such a much smaller city, residents of Austin seem to like using EVs much more!
Impact on Power load
Now, let us examine the impact of large-scale integration of EVs on total power load. We download the New York State real-time load data from NYISO's website http://www.nyiso.com/public/index.jsp. According to Wikipedia: ``An independent system operator (ISO) is an organization formed at the recommendation of the Federal Energy Regulatory Commission. In the areas where an ISO is established, it coordinates, controls and monitors the operation of the electrical power system, usually within a single US State, but sometimes encompassing multiple states." NYISO governs the operation of the electrical power system in New York State.
We build an interactive plot using Shiny to show the aggregation of the EV load and base load. The base load is the power load without EV charging load. The time interval is 5 minutes. There are a total of 288 intervals within a day. We can use the shiny sliderInput to select different numbers of EVs needed to be charged in NYC. Each EV requires about 36 kW power to charge. The interactive plot shows the aggregation of the EVs and the base loads. To design a smart charging strategy, people should charge their EVs when the electricity price is low.
Price Data
So, let us visualize the real-time price data. We plot the real-time electricity price as a function of time of day (5-minute interval). The real-time price data is downloaded from https://hourlypricing.comed.com/. The data format is JSON and we parse the data to extract price information as a function of time. After data parsing, we store the information in CSV format for later use.
Generally speaking, the electricity price is relatively low from midnight to 3:00 AM, which may be the best time to charge your EV. It is interesting to see that there are two price peaks during the time period from the 200-th to the 250-th time intervals (4:00PM to 9:00PM), which indicates that the power load is maximized in the evening and so is the real-time price. Thus, you probably don't want to charge your EV when you come home after work!
Using the interactive plot, we can visualize the aggregation of the EV charging and power loads for different numbers of EVs and the variation of the real-time electricity price. Apparently, we should charge our EVs when the price is low, i.e., around midnight. Can a utility company design an incentive charging strategy to incentivize customers to charge their EVs during a certain period of time? In the following, we propose such machine learning algorithm to schedule EV charging to reduce charging cost and improve power operation efficiency.
Charging Control of EVs Using Online Learning
Our idea is to use the flexible load capability offered by EVs owned by residential customers. Large-scale integration of EVs may impose a significant burden on the grid, leading to effects such as the creation of new peaks, peak load amplification and voltage deviations. To cope with these issues, many algorithms have been proposed to schedule the charging of EVs. In our formulation, we model the distribution power company and every EV customer as an individual decision maker who wishes to optimize his own utility function. For the distribution power company, the payoff is maximized if the total load profile over a day is valley-filling.
A non-valley filling total load profile (left) may overload the power plants at peak hours. On the other hand, a valley filling load profile (right) does not overload power plants at peak hours. Distribution power company does not want to overload power plants, nor does want a non-valley-filling total load profile. On the other hand, for the EV customer, the utility function is maximized if the cost to charge the EV over a day is minimized. By designing a suitable pricing policy, the distribution company aims at ensuring that the aggregate charging profile adopted by the customers is valley-filling.
Distributed Charging Control Algorithm
Our distributed charging control algorithm is based on an online learning and online convex optimization framework. The online learning framework has now assumed tremendous popularity in the online convex optimization and machine learning communities. We use a regret minimization algorithm in the online learning framework. The regret minimization algorithm uses the regret as the performance measure and provides an iterative way for every decision maker to update its policy such that, at convergence, the policy is optimal in a suitably defined sense.
In particular, the objective of the distribution company is to achieve a total load profile that is valley-filling while ensuring that both the inflexible base load and the schedulable EVs are supplied with the required amount of energy. Thus, it wishes to obtain the aggregated charging profile that solves the optimization problem described below.
To incentivize the customers to choose charging profiles that in aggregate minimize the cost, the distribution company designs suitable pricing profiles for the energy being supplied to the EVs. Every EV customer fixes the charging schedule at the beginning of the day based on the information about its own constraints and any information provided by the distribution company.
Charging Cost
A price-sensitive EV customer seeks to minimize the total cost of charging by suitably shaping its charging schedule. Thus each customer wants to solve the optimization problem described below.
We adopt the optimistic mirror descent (OMD) algorithm to generate the charging profile update which minimizes the regret. On each day, the regret minimization algorithm generates the charging profile update without knowing the current objective function (and its gradient). Specifically, the OMD algorithm iteratively applies the updates as follows.
By implementing our charging control algorithm, we can show that both distribution company and customer regrets will converge to zeros. The following figure summarizes the workflow of our algorithm. Assume that the distribution company and its customers want to schedule EV charging on Wednesday, then
We consider a toy example with 20 EVs. Figure below shows that with appropriately scheduling the EV charging, a valley-filling load profile is obtained.
Conclusions
We have presented a novel framework for distributed charging control of EVs using online learning with Shiny for interactive data visualization. The proposed algorithm can be implemented without low-latency two-way communication between the distribution company and the EV customers, which fits in with the current communication infrastructure and protocols used in the smart grid. For the reader who is interested in the math behind our algorithm, one can find the details in our journal paper at my website.
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