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Management of Load A. Cost Model This research utilizes two cost models: One cost model only considers the generator cost and the other one considers both the generator cost and emission cost in its modeling, as shown in (1) - (3): 2 𝐺𝑖 = 𝑎𝑖 𝑃𝐺,𝑖 + 𝑏𝑖 𝑃𝐺,𝑖 + 𝑐𝑖 , 𝑖 = 1,2 … 𝑁𝐺 (1)

Where 𝑃𝐺,𝑖 , is the output power of generator 𝑖, 𝑎𝑖 , 𝑏𝑖 , 𝑐𝑖 are the related coefficients of the generator in the quadratic cost model; 𝑁𝐺 is the total quantity of generators in the system. 𝑒𝑖 = 𝑃𝐶𝑂2 × 𝐸𝐹𝐶𝑂2 ,𝑖 , 𝑖 = 1,2 … 𝑁𝐺 (2) 2 𝐸𝑖 = 𝑎𝑖 𝑃𝐺,𝑖 + 𝑏𝑖 𝑃𝐺,𝑖 + 𝑐𝑖 + 𝑒𝑖 𝑃𝐺,𝑖 , 𝑖 = 1,2 … 𝑁𝐺 (3)

Where 𝑒𝑖 represents the quantified cost of generator emissions; 𝑃𝐶𝑂2 is the emission price of 𝐶𝑂2 and 𝐸𝐹𝐶𝑂2 ,𝑖 represents the quantified value of emission of generator 𝑖; 𝑒𝑖 𝑃𝐺,𝑖 represents the emission cost section in the combined cost model. B. Temporal and Spatial Load Management (TSLM) This load management method is formulated to optimize the load distribution on both the temporal and spatial frame for a targeted bus network. The objective function of TSLM is: 𝑁

𝐶 = min ∑𝑖 𝐺 𝐺𝑖 (4) Where the 𝐺𝑖 represents the generator cost, 𝑁𝐺 is the number of generators and 𝐶 is total cost of generator. If the emission is taken into account in the object, the cost model of (1) will be taken place by the combined cost model of (3). Then the objective function becomes: 𝑁

𝐶 = min ∑𝑖 𝐺 𝐸𝑖 (5) As each node in the area has a certain amount of controllable load capacity, the load at each bus would have a maximum value and a minimum value for every hour as shown in (6). 0,𝑚𝑖𝑛 0,𝑚𝑎𝑥 𝑃𝐿,𝑖,ℎ ≤ 𝑃𝐿,𝑖,ℎ ≤ 𝑃𝐿,𝑖,ℎ , 𝑖 = 1,2 … 𝑁𝐵 (6)

Where 𝑃𝐿 is the power at a specific bus 𝑖; 𝑃𝐿0 is the load demand of the base case and 𝑁𝐵 is the number of buses in the simulated network. The ℎ represents the hour and H serves as the total hours for optimization. The min and max superscripts define the lower bound and upper bound of the power. All the generators’ status in the optimized case should be under their set-up limits in (7).

0,𝑚𝑖𝑛 0,𝑚𝑎𝑥 𝑃𝐺,𝑖, ≤ 𝑃𝐺,𝑖 ≤ 𝑃𝐺,𝑖 , 𝑖 = 1,2 … 𝑁𝐺 (7)

Where 𝑃𝐺 is the power of a specific generator 𝑖; 𝑃𝐺0 is the generator power of the base case and 𝑁𝐺 is the number of generator in the simulated network. The total amount of optimized load demand in one day is kept to be constant as given in (8). 𝑁𝐺 0 𝑁𝐵 𝐻 ∑𝐻 ℎ=1 ∑𝑖=1 𝑃𝐿,𝑖,ℎ = ∑ℎ=1 ∑𝑖=1 𝑃𝐿,𝑖,ℎ (8)

E. Total Cost and Emission The TSLM load management method would produce improved load distribution from the base case. The new LMP at each bus can then be calculated by employing the optimal power flow (OPF) function in MATPOWER using the hourly load values in the simulated cases. Therefore, the overall cost 𝐶 and the total carbon dioxide emission 𝐸𝐶𝑂2 can be calculated based on the TSLM results by (9) and (10), respectively. 𝑁

𝐵 𝐶 = ∑𝐻 ℎ=1 ∑𝑖=1 𝐿𝑀𝑃𝑖,ℎ × 𝑃𝐿,𝑖,ℎ (9)

𝑁

𝐺 𝐸𝐶𝑂2 = ∑𝐻 ℎ=1 ∑𝑖=1 𝑃𝐺,𝑖,ℎ × 𝐸𝐹𝐶𝑂2 ,𝑖 (10)

Algorithm Implementation And Simulation A. Cost Model Based on the generator cost data from EIA [find citation], the parameters of the generators quadratic cost model can be obtained as given in Table I. Table I GENERATOR COST MODEL PARAMETERS Fuel Type a b c

Coal 0.035 31 200

Natural Gas 0.04 46 300

Oil 0.05 240 400

According to the social cost of carbon (SCC) estimated by United States Environmental Protection Agency (EPA) in 2013 [find citation], the price of carbon dioxide is set at 10 $/ton. Based on the EIA’s data, the emission factors of different types of generators are listed in Table II. Due to the various emission factors of natural gas, the emission factors for natural gas generators are set to two typical values, as shown in Table II, based on the EIA’s data. Table II CARBON DIOXIDE EMISSION PARAMETERS

Fuel Type 𝐸𝐶𝑂2 (lbs/MWh) 𝑒 ($/MWh)

Coal 2159 9.72

Natural Gas 934/1450 4.20/6.53

Oil 1911 8.60

As the simulation is going to be tested in the modified 5 bus, 5 gen case based on PJM 5-bus system which is based on data from F.Li and R.Bo, "Small Test Systems for Power System Economic Studies" from the Proceedings of the 2010 IEEE Power & Energy Society General Meeting, the fuel types and emission factors of each generator in the system are set as shown in Table III. Table III GENERATOR FUEL TYPES AND EMISSION FACTORS Generator Number 1 2 3 4 5

Bus Number 1 1 3 4 5

Fuel Type Coal Natural gas Natural gas Oil Oil

𝐸𝐹𝐶𝑂2 (lbs/MWh) 2159 934 1450 1911 1911

B. Base Case Formulation The TSLM load management method is tested on the modified 5 bus system. The rudimentary 24-hour load profile in the case is constructed based on the data from one of the PJM daily hourly loads [29], shown in Fig. 3.

The simulation assumes that all the nodes follow the identical load ratio for 24 hours and the loads at all the buses have same type of load profile over the 24-hour period. To put into consideration of the randomness in consumers’ activities and their different behaviors, the hourly load at each node can vary following normal distribution between -3% and 3%. ±10% of controllable load is assumed to be acceptable at each bus.

C. Base Case without Load Management The LMPs of the base case is obtained via MATPOWER, as shown in Fig. 4. As shown in the figure, without load management there are two LMP peaks appearing at around 10 AM and 8 PM which are consistent to the load peaks in Fig.3. If there is no transmission congestion in the control area, the LMPs in this area should be the same. But in Fig.4 the LMPs at buses 1, 2 and 3 are lower than the other buses’ around 10 AM and 8 PM indicate some congestions occurred. [Add about co2 emissions as well]

D. Temporal and Spatial Load Management The result of TSLM is shown in Fig. 5. By comparing Figs. 4 and 5, it is clearly seen that at around 10 AM and 8 PM the LMPs in Fig. 4 are almost 4 times of the LMPs before using the TSLM in Fig. 5, which means the TSLM has eliminated congestion and reduced the peaks in load demands. [Add about co2 emissions as well] E. Emission Comparison

CONCLUSIOIN This paper compared the TSLM method against a system without any load management method. The TSLM allows dispatching loads in both space and time frames. The simulations were conducted on the modified IEEE 5-bus system to observe the effects of TSLM on load management in terms of its CO2 emissions reductions. The results show that TSLM effectively reduces the CO2 emissions in a 5-bus system.