# Design Of Experiments, Industrial Engineering,ANOVA Table Excel, Data Analysis

Guidelines for the project on “Analyzing the Impact of network topology and emissions control related parameters on the performance of an electric network.”

Abstract:

Coal fired electric generators contribute to 35-40% of the carbon dioxide released to the atmosphere in the U.S. Among the CO2 emissions reduction programs, cap-and-trade (C&T) is one of the most used policies. Economic studies have predicted that C&T policies for electricity networks, while reducing emissions, will likely increase price and decrease consumption of electricity. This project seeks to create a model to develop Pareto optimal designs for CO2 cap-and-trade policies. The performance measures that are considered for the purpose of design are social welfare and the corresponding system marginal price (MP), CO2 emissions, and electricity consumption level, among others. An analysis of variance with the selected factors: policy related factors (initial allowance cap, cap reduction rate, violation penalty) and network related factors (congestion, social cost of carbon, and demand-price sensitivity of the consumers) can be performed to assess their impact on the performance measures.

Project Objective: To analyze the impact of policy and network related factors on the performance of the electricity network measured by social welfare, total carbon emissions, total electricity consumption, and average electricity prices.

To address the above objective, you can apply the techniques you have learned in the class (Factorial/ fractional factorial experiments, linear and non-linear regression).

Read the paper “Design of Pareto optimal CO2 cap-and-trade policies for deregulated electricity networks” for a better understanding of the experimental context.

Input Parameters:

· Emissions factor (epsilon 1, 2, 3): This are fixed parameter utilized to calculate carbon emissions. Generator 1 and 3 have an emissions factor of 1 which indicates that they produce one ton of CO2 for each MWh of electricity produced. Generator 2 has emission factor equal to zero (green generator). You can play with the value of these parameters.

· Year: A parameter that takes values from 1 to 30, representing a 30 year planning horizon.

· A: Represents the total number of tons of CO2 at the beginning of the horizon (Cap). The amount is reduced year by year (according to the reduction rate factor) after the fifth year.

Factor to be analyzed in ANOVA:

· Cap reduction rate (red): This is the yearly percentage reduction of the cap. Reduction rate can take values from 0 to 1

· Emissions cap (cap): This is the limit (cap) for carbon emissions at any year. It is affected by the reduction rate (red).

· Emissions penalty (p): This is the penalty that generators must pay if they exceed the allowances emissions allocated.

· Social cost of carbon (SCC): This parameter indicates the cost to society for every ton of CO2 released to the atmosphere (SCC).

· Demand sensitivity (B4): This is the demand price sensitivity (slope of the demand curve). The paper assumes values of 0.025, 0.05, and 0.075. You are not limited to these values.

· Transmission line capacity (f): This is the capacity of the transmission lines (that may lead to congestion). The paper assumes that the capacity of lines 1 and 4 (c1, c4) are modified as follow: c1=c4 =120; c1=c4 =100; c1=c4 =80. You can choose to modify other lines’ capacities and in a different amount. (If the network becomes infeasible, you will know.)

Outputs:

· Generator production (q1, q2, q3): Represent the power in MWh produced by each generator. Generator 2 (q2) is green and does not generate carbon emissions.

· Electricity price (u1.l): Represent the system marginal price of electricity in \$/MWh (dual variable). This is the price that consumers pay for electricity as a result of the minimization of the social cost by choosing the electricity dispatch.

· Carbon price (l20.l): Represent the price associated to the carbon emissions once the problem has been solved (\$/tCO2). This is also a dual variable of the optimization model.

From these outputs, the yearly and total horizon (cumulative) carbon emissions can be calculated. The total consumption in the network can be found by adding the production of each generator (yearly or for the horizon). Other outputs to analyze can be, for example, generators’ profit, generators’ penalty, and their bidding behavior. Students are welcome to modify the output file if other measures are going to be analyzed. Look at the code line:

put p,B4,red,cap,f,t,year,q1.l, q2.l,q3.l, u1.l,A,l20.l,epsilon1,epsilon2,epsilon3;

The General Algebraic Modeling System (GAMS) is specifically designed for modeling linear, nonlinear and mixed integer optimization problems. The system is especially useful with large, complex problems. GAMS is available for use on personal computers, workstations, mainframes and supercomputers.

GAMS allows the user to concentrate on the modeling problem by making the setup simple. The system takes care of the time-consuming details of the specific machine and system software implementation.

GAMS is especially useful for handling large, complex, one-of-a-kind problems which may require many revisions to establish an accurate model. The system models problems in a highly compact and natural way. The user can change the formulation quickly and easily, can change from one solver to another, and can even convert from linear to nonlinear with little trouble.

· An introduction to GAMS can be found in: http://www.gams.com/docs/intro.htm.

http://www.gams.com/dd/docs/bigdocs/GAMSUsersGuide.pdf.

· A simple example can be found at : http://www.gams.com/docs/example.htm

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