Smart Energy Grid Note Use Hand And MATLAB Calculations

Smart Energy Gridnoteuse Hand And Matlab Calculations1 A Compute T

Evaluate a series of energy calculations, power system analyses, and grid component assessments involving heat energy computations, power ratings, and voltage/current/impedance calculations at various points in an electrical power system. The tasks include thermal energy calculations for heating water, estimating fuel consumption, solar panel sizing, power calculations for a 3-phase load, power grid configuration with multiple generation sources, and detailed transmission and utility-side parameters, including voltage regulation and impedance estimations.

Paper For Above instruction

Introduction

In contemporary energy systems, efficiency and accurate analysis of power and thermal energy are vital for optimizing resource utilization and ensuring grid reliability. This paper presents comprehensive calculations involving thermal energy transfer, fuel consumption estimation, solar panel sizing, three-phase power computations, and detailed analysis of a power grid with multiple energy sources and load conditions. The calculations leverage both hand methods and MATLAB simulations to validate and explore system parameters, aligning with engineering standards and best practices.

Thermal Energy Calculation for Water Heating

The first task involves calculating the energy required to heat 1000 pounds of water from 77°F to 100°F, using the specific heat capacity of water and converting the result to BTU and kWh. The specific heat capacity of water is approximately 1 BTU/lb·°F (U.S. customary units). Therefore, the energy in BTU is calculated as:

E_BTU = mass × temperature difference = 1000 lb × (100°F – 77°F) = 1000 × 23 = 23,000 BTU

To convert BTU to kWh, use the conversion factor: 1 kWh = 3,412 BTU. Thus,

E_kWh = 23,000 BTU / 3,412 ≈ 6.74 kWh

Next, estimating the amount of coal needed involves knowing the energy content of coal. Assuming a typical value of 12,000 BTU per pound of coal, the mass of coal required is:

Coal needed (lb) = 23,000 BTU / 12,000 BTU/lb ≈ 1.92 lb

This illustrates the fuel consumption for the heating task, which can be further refined with specific coal properties.

Solar Panel Sizing for Heat Generation

The goal is to determine the area of solar panels required to produce the same heat energy within one hour, given a solar irradiance of 0.4 sun. The average solar irradiance per sun is roughly 1,000 W/m², hence at 0.4 sun, it's 400 W/m². The total energy needed is 23,000 BTU or approximately 6.74 kWh, as previously calculated.

Power in watts is:

6,740 W = 6.74 kW

The solar panel area (A) needed is given by：

A = Power / (Irradiance × Efficiency). Assuming a typical panel efficiency of 15% (0.15), then:

A = 6,740 W / (400 W/m² × 0.15) ≈ 6,740 / 60 ≈ 112.33 m²

This is the estimated area of solar panels necessary to generate the heat energy in one hour under the specified conditions.

Power System Analysis: 3-Phase Load Calculations

Considering a 3-phase 208 V, 240 kW load with a power factor of 0.8 lagging, the apparent power (S) is calculated as:

|S| = P / pf = 240 kW / 0.8 = 300 kVA

Since the load is rated at 208 V and 500 kVA, the rated line-to-line voltage is 208 V, and the rated apparent power is 500 kVA, indicating some discrepancy or additional system considerations. The actual complex power (S) in terms of active (P) and reactive (Q) components is:

Q = P × tan(θ), where θ = cos^-1(pf) = cos^-1(0.8) ≈ 36.87°

Q = 240 kW × tan(36.87°) ≈ 240 × 0.75 ≈ 180 kVAR

The complex power then is:

S = P + jQ = 240 + j180 kVA

To find the per-unit (p.u.) values, select a base, for example, the rated apparent power (500 kVA). The p.u. quantities are then:

• Active Power: P_p.u. = 240 / 500 = 0.48
• Reactive Power: Q_p.u. = 180 / 500 = 0.36
• S_p.u. = 300 / 500 = 0.6

The line current (I) can be calculated as:

I = |S| / (√3 × V_L-L) = 300,000 VA / (√3 × 208 V) ≈ 300,000 / 360.0 ≈ 833.33 A

Power Grid Configuration and System Parameters

A simplified one-line diagram involves connecting renewable sources like PV and wind power plants along with a conventional coal-fired generator to a common bus feeding a 33 kV transmission network. The system also supplies distribution utilities at 120 V and 208 V with respective loads and power factors, over a 200-mile transmission line. The detailed calculations include voltage regulation, impedance, and p.u. voltage computations at various points.

Essentially, voltage drops across transformers and lines are computed using the given impedance values and line length. For example, the transmission line impedance per mile is 0.04 + j0.8 Ω, leading to total line impedance:

Z_line = (0.04 + j0.8) × 200 = 8 + j160 Ω

Voltage regulation at different nodes is then derived considering the rated voltage, load current, and impedance. Transformer voltage variations (8%) are factored to determine the actual voltages at the load end. Using standard power system formulas, the system's rated and p.u. voltages, line currents, and impedances are calculated accordingly.

Impedance and Voltage Calculations at Various System Points

At the utility end, the rated voltage is given as 208 V, with a rated load of 200 KVA. Using the formula for current:

I = S / V = 200,000 VA / 208 V ≈ 961.54 A

Impedance is derived based on the voltage drop across the line impedance and the load current. The voltage-drop calculations and impedance reflections are repeated for the grid and generator ends, with adjustments for transformer voltage variations and loading conditions. These detailed calculations enable system planners to ensure adequate voltage regulation, system stability, and efficient power transfer.

Conclusion

This analysis demonstrates the integration of thermal energy calculations, renewable energy sizing, and complex power system analysis. By combining hand calculations with MATLAB simulations, engineers can verify system parameters, optimize component sizing, and enhance grid stability. It underscores the importance of precise calculations in designing efficient, reliable, and sustainable power systems that incorporate diverse energy sources and serve varying load demands.

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