代做ENGR301 FF 25F代写Matlab编程

ENGR301 FF 25F

Team Project

Due date: See Moodle

1. Introduction

The Moses-Saunders Power Dam was built in 1959 and spans the entire width of the Saint Lawrence River between Cornwall, Ontario and Massena, New York. This massive joint Canadian and American-operated dam is 60 meters tall and is 979 meters long and provides three important functions which must constantly be balanced to their most efficient overall outcomes. A description of the operation of the dam can be viewed here. A 1960’s documentary about the construction of the dam can be viewed here.

The primary function of the dam is to generate electrical power with two generating stations that are located on each side of the dam. On the Canadian side, the power generation turbines in the R.H. Saunders station provides a maximum capacity of 1045 MW of power for Ontario Power Generation (OPG), while a maximum of 912 MW is generated for the American side in the Robert Moses dam. This occurs when the hydraulic head is at its maximum level and when the sluice gates are fully open. Sluice gates control the flow of water through the dam, and they can either be fully closed, fully open, or partially open at any given time.

•    Closing the gates will reduce the flow of water from Lake Ontario and reduce the amount of power generated in the station.

•    Opening the gates will increase the flow of water from Lake Ontario and raise the amount of power generated in the station.

•    Hydraulic head is the difference in the water levels upstream and downstream of the dam.

•    Power is disposed of the moment that it is generated, and the price of electricity varies depending on the time of day.

The second function of the dam is to allow shipping through the Saint Laurence Seaway on waters that are stable and deep enough to accommodate freighters that are specifically designed to navigate through it. Several dangerous rapids also disappeared in the process, eliminating the need for several century-old canal locks which are now either tourist destinations or are underwater. Deeper waters mean that ships can carry more cargo without the risk of hitting the bottom. Shipping companies are charged to go through the seaway as a function of their total weight including cargo.

•    Withholding water will raise the water level upstream and reduce it downstream.

•    Releasing water will reduce the water level upstream and raise it upstream.

The third function of the dam is to provide steady river water levels to municipalities upstream and downstream of the dam and ensure that the water levels are sufficient to prevent flooding and allow water activities in the area, including boating. The dam also controls the level of Lake Ontario.

Finally, the operation of the dam is highly dependant on precipitation:

•    Low precipitation reduces the level of water upstream and downstream of the dam.

•    High precipitation increases the level of water upstream and downstream of the dam.

•    The weather, of course, is uncontrollable. However, weather predictions and historical trends can assist planners in developing case scenarios to mitigate risks.

The International Lake Ontario – St. Lawrence River Board (ILO-SLRB) determines weekly water flow to balance power generation, maritime navigation, and environmental needs, meaning water flow, and thus power output, is not constant. As a member of that board, you are tasked with creating a model which will optimize the past year of operation of the gates to prepare for future climate events. Fortunately, your team may use data from the 2024 operating year to arrive to the best decision on deciding when to open or close the sluice gates in the hypothetical situation.

2. Project Objective

The objective of this project is to theoretically maximize revenue that could have been obtained over the past year (January 1st, 2024, to December 31st, 2024) via the sale of electrical power by the R.H. Saunders Power dam to OPG (Canadian side only) while respecting minimum and maximum water levels on the river, both upstream and downstream.

This can be done by analysing the hourly or daily fluctuations of:

• Saint Lawrence river water levels,

• Lake Ontario water inflow,

• Electrical power rate fluctuations,

•    Any other input data that can contribute to the analysis.

To accomplish this, you will need to create a daily or hourly revenue model in Excel or Matlab and determine the position of the sluice gate for every time frame which will obtain the highest revenues while staying between acceptable water level limits both upstream and downstream of the dam. This project is divided into two components:

3.      Actual revenues from power generation for the year 2024:

3.1. R.H. Saunders Power Generating Station

The Moses-Saunders Dam has a maximum head (water height difference) of 25 meters . The sluice gates on the Canadian and American sides of the dam are always open to the same percentage. The equation for hydraulic power generation is:

Where,

P      Power generation (W)

x      Sluice gate fraction open (0 = closed, 1 = open)

ρ      Density of fresh water (998 kg/m3)

Q      Water flow through the dam (m3/s)

g      Gravity (9.81 m/s2)

h      Dam hydraulic head (m)

E      Energy Generation (J)

t      time (s)

This equation can be used to calculate the maximum water flow through the Canadian side of dam, knowing that in that situation the sluice gates are fully open. Any extra flow is channeled  through the nearby Long Sault Dam, which does not produce power but is only used to regulate the water level of Lake Saint Lawrence and to bleed off any excess flow.

The committee sets water flow from Lake Ontario, which eventually ends up in the dam. The set water flow is found at the top of this webpage, or here.

The water levels on either side of the dam are recorded in the following web pages, under Bulk Data Export:

• Long Sault Dam (upstream of Moses-Saunders dam)

• Cornwall (downstream of Moses-Saunders dam)

The “ Datum” corresponds to the normal elevation above sea level, and recorded values are deviations from that datum at any point in time (negative or positive).

a)   Plot the power (in MW) and energy (in GJ) generated for OPG by the Saunders Dam from January 1st to December 31st, 2024.

b)   Plot the amount of river water overflow that was sent through the Long Sault Dam over the same period.

3.2. Sale of Electrical Power to Ontario Users

The electricity produced at the R.H. Saunders Generating Station (on the Canadian side) is sent to the OPG grid and is sold to residential and non-residential clients throughout Ontario. The price of electricity depends on the rate plan that is selected but in 2024, over 96% of clients

used Time-of-Use (TOU) pricing. Revenues can therefore be estimated by considering that all power sales are sold under that rate plan. The rates are modified annually, and the rates that were in effect on January 1st, 2024, were updated on November 1st, 2024. All information about rates over the study period can be found here.

c)   Determine the revenues from the sale of electricity generated at the R.H. Saunders Generating Station in 2024, assuming that all the generated power was sold to customers in Ontario.

4.   Power Generation Optimization for 2024

In this section, you are tasked to determine how much power could have been generated had you had full knowledge of upstream water levels and flows over the entire period covering January 1st to December 31st, 2024. To accomplish this, an approximative correlative model must be created linking flow and water levels.

There exist lower and upper limits to water levels both upstream and downstream of the dam. To accomplish this, a simple model must be built which estimates these levels as a function of flows based on the data obtained over the 2024 period.

The historical limits of the water levels for each period of the year are shown in a chart on this webpage. In the optimization, water levels cannot exceed the minimum or maximum per period. In the same capacity, the flow in the river (Lake Ontario Outflow) cannot exceed the minimum and maximum historical outflows shown here.

d)   Calculate and plot an alternate reality for 2024 in which the Lake Ontario outflow is adjusted to maximize profitability from electricity sales in that year.

5.   Deliverable

In groups of 1 to 3 students, please submit a report of 10 pages or less in PDF format explaining calculations and correlations and presenting plots that optimize the amount of revenue generated by the sale of electricity from dam in Ontario over the entire year 2024, without considering interest or inflation.

Grading Criteria:

Data usage	20%
Calculations	20%
Correlations	20%
Figures and tables	10%
Report Quality	10%
Revenue Optimization score	20%