Problem 1 (Source, Load and Battery). In the figure shown, a DC energy source generates power Pe to a bus with a load and a battery. At any instant in time the battery is represented by a voltage source E, and an internal resistance R, as shown. It is connected to the grid by Bidirectional DC/DC converter which we assume ideal, with no power losses and V, = kV, with k > 0 constant. The voltage E, depends on the state of charge of the battery, but let's assume it constant. Pe P DC/DC Load E DC/DC Bidirectional Vg = kV, Q1: Let the gain of the DC/DC Bidirectional be k =1 (ie assume it is not there). Determine an expression for the voltage V in terms of the powers generated and delivered to the load (Pe,P, ) and the battery voltage and resistance E3,R3. (Hint: simple DC circuit analysis and solve a quadratic equation. All voltages are positive); Q2: using the expression in Q1, let the power generated be Pe = 5.0kW and the battery be such that E, = 40.0V , R2 =0.052. What is the maximum power you can deliver to the load? (Hint: max P, for which the quadratic equation has real solution);

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Please solve only Q3.

Problem 1 (Source, Load and Battery).
In the figure shown, a DC energy source generates power Pg to a bus with a load and a battery.
At any instant in time the battery is represented by a voltage source E, and an internal
resistance R, as shown. It is connected to the grid by Bidirectional DC/DC converter which we
assume ideal, with no power losses and V3 =kV, with k > 0 constant. The voltage ER
depends on the state of charge of the battery, but let's assume it constant.
Pa
DC/DC
Vo
Load
+
E
DC/DC
Bidirectional
V = kV,
Q1: Let the gain of the DC/DC Bidirectional be k =1 (ie assume it is not there). Determine an
expression for the voltage V, in terms of the powers generated and delivered to the load
(Pe,P, ) and the battery voltage and resistance E3,R3- (Hint: simple DC circuit analysis and
solve a quadratic equation. All voltages are positive);
Q2: using the expression in Q1, let the power generated be Pe =5.0kW and the battery be
such that E, = 40.0V , R2 =0.052. What is the maximum power you can deliver to the load?
(Hint: max P, for which the quadratic equation has real solution);
Q3: in most applications the bus voltage V, is set to be consistent with the grid, and we use the
DC/DC Bidirectional to interface to the battery. Let the bus voltage be set to V = 200.0V , the
battery is the same as in Q2, the power generated be again P = 5.0kW and the power to the
load be P, = 6.0kW . Determine the value of the gain k > 0 for the converter (Hint: use DC
circuit analysis similar to Q1, which leads to a quadratic equation in k. Choose the solution
which yields smaller current I )
Transcribed Image Text:Problem 1 (Source, Load and Battery). In the figure shown, a DC energy source generates power Pg to a bus with a load and a battery. At any instant in time the battery is represented by a voltage source E, and an internal resistance R, as shown. It is connected to the grid by Bidirectional DC/DC converter which we assume ideal, with no power losses and V3 =kV, with k > 0 constant. The voltage ER depends on the state of charge of the battery, but let's assume it constant. Pa DC/DC Vo Load + E DC/DC Bidirectional V = kV, Q1: Let the gain of the DC/DC Bidirectional be k =1 (ie assume it is not there). Determine an expression for the voltage V, in terms of the powers generated and delivered to the load (Pe,P, ) and the battery voltage and resistance E3,R3- (Hint: simple DC circuit analysis and solve a quadratic equation. All voltages are positive); Q2: using the expression in Q1, let the power generated be Pe =5.0kW and the battery be such that E, = 40.0V , R2 =0.052. What is the maximum power you can deliver to the load? (Hint: max P, for which the quadratic equation has real solution); Q3: in most applications the bus voltage V, is set to be consistent with the grid, and we use the DC/DC Bidirectional to interface to the battery. Let the bus voltage be set to V = 200.0V , the battery is the same as in Q2, the power generated be again P = 5.0kW and the power to the load be P, = 6.0kW . Determine the value of the gain k > 0 for the converter (Hint: use DC circuit analysis similar to Q1, which leads to a quadratic equation in k. Choose the solution which yields smaller current I )
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