Consider the circuit representation of a 2-bus electric power system with a short and lossless line...

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Consider the circuit representation of a 2-bus electric power system with a short and lossless line shown in Figure 1. We will explore the qualitative behavior of the system as the load changes, under what conditions the power flow can be solved, and how reactive power affects the ability of the system to deliver active power to the load. The generator is modeled as a fixed voltage source of magnitude E, and its voltage phase angle is the reference, set to zero. E = E20 + jX V = V20 P + jQ Figure 1: Single-line diagram of a 2 bus system. (a) For this system, write out the power flow equations at the load bus that describe the active and reactive power absorbed by the load. State the unknowns in these equations that are to be solved for. = (b) For parts (b) through (g), use E = 1 p.u. and X = 1 p.u. for the system parameter values. Eliminate the load bus voltage angle variable from the equations derived in (a) to obtain an expression of the form f(V, P, Q) = 0 that relates the load bus voltage to the load active and reactive power (Hint: your solution should be a quadratic equation in V²). (c) For load values of P = 0.25 p.u., Q = 0.25 p.u., how many physically feasible solutions (if any) can be found for V that satisfy f(V, 0.25, 0.25) 0? (d) Repeat the same exercise as part (c), but with load values of P = 0.25 p.u., Q = -0.25 p.u., and report how many physically feasible solutions (if any) can be found for f(V, 0.25, -0.25) = 0. (e) From the expression derived in part (b), find a condition that guarantees the existence of at least one solution to the power flow problem. Comment on whether the load values from parts (c) and (d) satisfy the condition just derived. Consider the circuit representation of a 2-bus electric power system with a short and lossless line shown in Figure 1. We will explore the qualitative behavior of the system as the load changes, under what conditions the power flow can be solved, and how reactive power affects the ability of the system to deliver active power to the load. The generator is modeled as a fixed voltage source of magnitude E, and its voltage phase angle is the reference, set to zero. E = E20 + jX V = V20 P + jQ Figure 1: Single-line diagram of a 2 bus system. (a) For this system, write out the power flow equations at the load bus that describe the active and reactive power absorbed by the load. State the unknowns in these equations that are to be solved for. = (b) For parts (b) through (g), use E = 1 p.u. and X = 1 p.u. for the system parameter values. Eliminate the load bus voltage angle variable from the equations derived in (a) to obtain an expression of the form f(V, P,Q) = 0 that relates the load bus voltage to the load active and reactive power (Hint: your solution should be a quadratic equation in V²). (c) For load values of P = 0.25 p.u., Q = 0.25 p.u., how many physically feasible solutions (if any) can be found for V that satisfy f(V, 0.25, 0.25) 0? (d) Repeat the same exercise as part (c), but with load values of P = 0.25 p.u., Q = -0.25 p.u., and report how many physically feasible solutions (if any) can be found for f(V, 0.25, -0.25) = 0. (e) From the expression derived in part (b), find a condition that guarantees the existence of at least one solution to the power flow problem. Comment on whether the load values from parts (c) and (d) satisfy the condition just derived. Consider the circuit representation of a 2-bus electric power system with a short and lossless line shown in Figure 1. We will explore the qualitative behavior of the system as the load changes, under what conditions the power flow can be solved, and how reactive power affects the ability of the system to deliver active power to the load. The generator is modeled as a fixed voltage source of magnitude E, and its voltage phase angle is the reference, set to zero. E = E20 + jX V = V20 P + jQ Figure 1: Single-line diagram of a 2 bus system. (a) For this system, write out the power flow equations at the load bus that describe the active and reactive power absorbed by the load. State the unknowns in these equations that are to be solved for. = (b) For parts (b) through (g), use E = 1 p.u. and X = 1 p.u. for the system parameter values. Eliminate the load bus voltage angle variable from the equations derived in (a) to obtain an expression of the form f(V, P, Q) = 0 that relates the load bus voltage to the load active and reactive power (Hint: your solution should be a quadratic equation in V²). (c) For load values of P = 0.25 p.u., Q = 0.25 p.u., how many physically feasible solutions (if any) can be found for V that satisfy f(V, 0.25, 0.25) 0? (d) Repeat the same exercise as part (c), but with load values of P = 0.25 p.u., Q = -0.25 p.u., and report how many physically feasible solutions (if any) can be found for f(V, 0.25, -0.25) = 0. (e) From the expression derived in part (b), find a condition that guarantees the existence of at least one solution to the power flow problem. Comment on whether the load values from parts (c) and (d) satisfy the condition just derived. Consider the circuit representation of a 2-bus electric power system with a short and lossless line shown in Figure 1. We will explore the qualitative behavior of the system as the load changes, under what conditions the power flow can be solved, and how reactive power affects the ability of the system to deliver active power to the load. The generator is modeled as a fixed voltage source of magnitude E, and its voltage phase angle is the reference, set to zero. E = E20 + jX V = V20 P + jQ Figure 1: Single-line diagram of a 2 bus system. (a) For this system, write out the power flow equations at the load bus that describe the active and reactive power absorbed by the load. State the unknowns in these equations that are to be solved for. = (b) For parts (b) through (g), use E = 1 p.u. and X = 1 p.u. for the system parameter values. Eliminate the load bus voltage angle variable from the equations derived in (a) to obtain an expression of the form f(V, P,Q) = 0 that relates the load bus voltage to the load active and reactive power (Hint: your solution should be a quadratic equation in V²). (c) For load values of P = 0.25 p.u., Q = 0.25 p.u., how many physically feasible solutions (if any) can be found for V that satisfy f(V, 0.25, 0.25) 0? (d) Repeat the same exercise as part (c), but with load values of P = 0.25 p.u., Q = -0.25 p.u., and report how many physically feasible solutions (if any) can be found for f(V, 0.25, -0.25) = 0. (e) From the expression derived in part (b), find a condition that guarantees the existence of at least one solution to the power flow problem. Comment on whether the load values from parts (c) and (d) satisfy the condition just derived.

Answer rating: 100% (QA)

a The power flow equations at the load bus can be written as follows Active Power Equation P V2 X Reactive Power Equation Q V2 X V2 X20 The unknowns i... View the full answer