Archive for December, 2008

Power Factor (3) – Finish

December 31, 2008

Correcting Your Power Factor
Some strategies for correcting your power factor are:

  • Minimize operation of idling or lightly loaded motors.
  • Avoid operation of equipment above its rated voltage.
  • Replace standard motors as they burn out with energy-efficient motors.
    Even with energy-efficient motors, however, the power factor is significantly affected by variations in load. A motor must be operated near its rated capacity to realize the benefits of a high power factor design.
  • Install capacitors in your AC circuit to decrease the magnitude of reactive power.

As shown in the diagram at above, reactive power (measured in kVARs) caused by inductance always acts at a 90° angle to real power. Capacitors store kVARs and release energy opposing the reactive energy caused by the inductor. This implies that inductance and capacitance react 180° to each other. The presence of both in the same circuit results in the continuous alternating transfer of energy between the capacitor and the inductor, thereby reducing the current flow from the generator to the circuit. When the circuit is balanced, all the energy released by the inductor is absorbed by the capacitor.
In the diagram below, the power triangle shows an initial 0.70 power factor for a 100-kW (real power) inductive load. The reactive power required by the load is 100 kW. By installing a 67-kW capacitor, the apparent power is reduced from 142 to 105 kVA, resulting in a 26% reduction in current. Power factor is improved to 0.95. In the “horse and railcar” analogy, this is equivalent to decreasing the angle the horse is pulling on the railcar by leading the horse closer to the center of the railroad track. Because the side pull is minimized, less total effort is required from the horse to do the same amount of work.
Capacitor suppliers and engineering firms can provide the assistance you may need to determine the optimum power correction factor and to correctly locate and install capacitors in your electrical distribution system.

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Source : Fact Sheet of Department of Energy USA

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Power Factor (2)

December 31, 2008
Cause of Low Power Factor
Low power factor is caused by inductive loads (such as transformers, electric motors, and high-intensity discharge lighting), which are a major portion of the power consumed in industrial complexes.

Unlike resistive loads that create heat by consuming kilowatts, inductive loads require the current to create a magnetic field, and the magnetic field produces the desired work. The total or apparent power required by an inductive device is a composite of the following:

  • Real power (measured in kilowatts, kW)
  • Reactive power, the nonworking power caused by the magnetizing current, required to operate the device (measured in kilovars, kVAR)

Reactive power required by inductive loads increases the amount of apparent power (measured in kilovolt amps, kVA) in your distribution system. The increase in reactive and apparent power causes the power factor to decrease.

Why Improve Your Power Factor?

Some of the benefits of improving your power factor are as follows:

  • Your utility bill will be smaller. Low power factor requires an increase in the electric utility’s generation and transmission capacity to handle the reactive power component caused by inductive loads. Utilities usually charge a penalty fee to customers with power factors less than 0.95. You can avoid this additional fee by increasing your power factor.
  • Your electrical system’s branch capacity will increase. Uncorrected power factor will cause power losses in your distribution system. You may experience voltage drops as power losses increase. Excessive voltage drops can cause overheating and premature failure of motors and other inductive equipment.

to be continued……..

Source : Fact Sheet of Department of Energy USA

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Power Factor (1)

December 31, 2008
Low power factor is expensive and inefficient. Many utility companies charge you an additional fee if your power factor is less than 0.95. Low power factor also reduces your electrical system’s distribution capacity by increasing current flow and causing voltage drops. This article describes power factor and explains how you can improve your power factor to reduce electric bills and enhance your electrical system’s capacity.

What is Power Factor?

To understand power factor, visualize a horse pulling a railroad car down a railroad track. Because the railroad ties are uneven, the horse must pull the car from the side of the track. The horse is pulling the railroad car at an angle to the direction of the car’s travel. The power required to move the car down the track is the working (real) power. The effort of the horse is the total (apparent) power.
Because of the angle of the horse’s pull, not all of the horse’s effort is used to move the car down the track. The car will not move sideways; therefore, the sideways pull of the horse is wasted effort or nonworking (reactive) power.
The angle of the horse’s pull is related to power factor, which is defined as the ratio of real (working) power to apparent (total) power. If the horse is led closer to the center of the track, the angle of side pull decreases and the real power approaches the value of the apparent power. Therefore, the ratio of real power to apparent power (the power factor) approaches 1. As the power factor approaches 1, the reactive (nonworking) power approaches 0.

Power Factor = Real Power / Apparent Power

For example, using the power triangle illustrated below, if
This indicates that only 70% of the current provided by the electrical utility is being used to produce useful work.
to be continued…………..
Source : Fact Sheet of Department of Energy USA

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Hydraulic Pump Power

December 31, 2008

The ideal hydraulic power to drive a pump depends on the mass flow rate, the liquid density and the differential height ……….

    either it is the static lift from one height to an other, or the friction head loss component of the system can be calculated as :

    Ph = q ρ g h / 3.6*10^6

    where :
    Ph = power (kW)
    q = flow capacity (m3/h)
    ρ = density of fluid (kg/m3)
    g = gravity (9.81 m/s2)
    h = differential head (m)

    Shaft Pump Power
    The shaft power – the power required transferred from the motor to the shaft of the pump – depends on the efficiency of the pump and can be calculated as

    Ps = Ph / η

    where :
    Ps = shaft power (kW)
    η = pump efficiency

    BHP (Brake Horse Power)

    BHP = (q x h x sg) / (3960 x eff)

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    PLCs and Fuzzy Logic (11) – Finish

    December 30, 2008
    Rule Decision Making and Outcome Determination

    The easiest way to formulate the rules for a fuzzy logic controller is to first write them as IF…THEN statements that describe how the inputs affect the outcome.

    Some fuzzy controllers are capable of handling two outputs at the same time, thus allowing two rules to be combined. For example, the rules:

    IF A = PS AND B = NS THEN C = ZR
    IF A = PS AND B = NS THEN D = NS

    can be combined into one rule:
    IF A = PS AND B = NS THEN C = ZR and D = NS

    This rule gives two outcomes, thus invoking two defuzzification processes, one for each controlling output. It is easiest, however, to create each rule individually (with only one outcome) and then combine them later.
    A fuzzy logic controller may or may not provide a choice of output membership function shapes (L, P, S, or Z). Moreover, it may or may not provide a choice about whether the functions are continuous or noncontinuous. However, before defuzzification occurs, all fuzzy controllers add the outcomes based on the appropriate rule logic. If the rule contains a logical AND function, the controller will select the lowest output value; if the rule contains an OR function, the controller will select the highest output value.
    If an application requires a highly accurate or smooth output, the rules should be designed so that an input condition triggers two or more rules. To do this, either the input membership functions must overlap or two input conditions must influence the same output.

    Defuzzification

    During the implementation of a fuzzy logic system, the system designer may be required to choose a defuzzification method, especially if the output membership function is noncontinuous.
    Defuzzification methods include the center of gravity (centroid), the left-most maximum, and the right-most maximum. If the selected defuzzification method is the center of gravity approach, the triggering rules must be arranged so that at least one rule is triggered at all times.
    Thus, there must always be an output from a rule. The controller will generate an error if there is no output due to a gap in input condition coverage (see Figure 14).

    CONCLUSION
    Fuzzy logic processing is a three-step procedure consisting of fuzzification, fuzzy processing, and defuzzification. Using this three-step process, a fuzzy controller can take vague nondiscrete input
    data and convert it into a specific output. This conversion process depends on the membership functions and rules established by the system designer during system implementation. When used correctly, fuzzy logic controllers can improve the performance of PLC systems that control both closed-loop and open-loop systems. They can also lead to the automation of tasks that previously required human intervention. Together, PLCs and fuzzy logic technology form a powerful tool for enhancing complex system automation.
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    PLCs and Fuzzy Logic (10)

    December 30, 2008
    Input/Output Determination
    Once the fuzzy system configuration has been established, the next step is to determine which inputs and outputs will be used in the fuzzy logic controller. The input conditions, or fuzzy input variables, must be able to be expressed by IF…THEN statements.

    That is, the input conditions to the fuzzy controller must be able to trigger conditional rules, meaning that they specify one or more output conditions. Inputs should be selected according to the process situations they describe. These variables should relate to similar process elements. If two inputs have little to do with each other, they will generate an outcome that is less effective than the outcome generated by two inputs that deal with the same element. For example, in a temperature-regulating batching operation, the batch temperature and tank jacket temperature both relate to the regulation of the steam valve output. By analyzing these two inputs together, a fuzzy controller can make a precise decision about how much to adjust the steam valve. An analysis of two unrelated inputs, such as batch temperature and liquid level, would not provide such an informed decision.

    Fuzzy Inference Engine
    The selection of the fuzzy inference engine encompasses the determination of how the fuzzification process will take place (e.g., the number and form of membership function, etc.), how the rules determine an outcome, and how the fuzzy controller implements defuzzification.
    Fuzzification
    The fuzzification process, which utilizes the membership functions defined by the user, assigns a grade to each fuzzy input received. This grade determines the level of outcome that will be triggered. Therefore, the shape of a fuzzy set’s membership functions is important, since this shape determines the input signals’ grades, which are mapped to the output membership function.
    Some fuzzy controllers allow the user to choose the shape of the membership functions by trial and error, while others have predefined membership function shapes. When using trial and error to determine the function shapes in a closed-loop fuzzy control system, the input membership functions should begin with overlapped L-shaped labels (see Figure 12). This ensures smoother control for the first trial due to the coverage provided by the L shape and the overlapping at the minimum and maximum points, which creates a balance (i.e., when one label grade is 1, the other is 0). The number of labels, or membership functions, that will form the fuzzy set is also an important part of the system design. For example, if a fuzzy set has five labels covering the same input data range as a three-label fuzzy set, the one with five labels will provide more fine-tuned control, especially if the output membership function also has five labels.


    Although membership functions do not have to be symmetrical, asymmetrical fuzzy sets should be carefully designed to ensure that they describe the fuzzy variable input properly. In Figure 13a, the inner membership functions provide more sensitivity near the zero label (from NS to PS) than at the NL and PL labels (from NL to NS and from PS to PL). Asymmetrical membership functions are typically used in open-loop system applications.

    Sometimes, a membership function in a fuzzy set may not provide any sensitivity between two labels. As illustrated in Figure 13b, the flat sections of the membership functions do not influence
    neighboring functions or the output. Therefore, the output will not change if the input variable falls in these regions.

    to be continued…………….

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    PLCs and Fuzzy Logic (9)

    December 30, 2008

    GUIDELINES FOR CONTROLLING COMPLEX SYSTEMS

    All fuzzy logic applications are different. However, certain design guidelines apply to all fuzzy logic systems. These guidelines provide the basic elements for the successful implementation of a
    fuzzy logic control system.

    They include:
    • control objectives
    • control system configuration
    • input/output determination
    • fuzzy inference engine design

    Control Objectives
    Fuzzy logic can be applied to virtually any type of control system, but it is especially suited for applications that rely heavily on human intuition and experience. The primary objective of applying fuzzy logic to an existing process is to improve the overall process and to automate tasks that previously required human judgment. In a new system, the primary objective of using fuzzy logic is to implement control that cannot be implemented using standard control methods. A system designer should not use fuzzy logic control just because it is available. Rather, the designer should use it because it will enhance the system. Otherwise, the outcome may not be enhanced; it may just become confusing.
    Typical applications of fuzzy logic involve batching systems and temperature control loops, where process control involves “tweaking” the output based on judgments about input conditions. For example, a temperature control loop application typically requires a knowledgeable operator who can regulate the control element based on decisions such as “if the temperature is a little high but all other inputs are OK, then turn the steam valve a little clockwise.” This rationale lends itself to fuzzy logic control.

    Control System Configuration
    The control objective leads to the selection of the fuzzy logic system configuration. There are several types of fuzzy configurations. Fuzzy logic does not have to be applied only in dedicated fuzzy control applications. It can also be used as a complementary system that supports another more conventional control method, such as a PID control loop. When used in this manner, the system is said to be a conventional fuzzy hybrid control system.

    to be continued………………

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    PLCs and Fuzzy Logic (8)

    December 30, 2008
    Membership Functions and Rule Creation
    To provide enhanced resolution and accuracy, this system uses five–membership function (fivelabel) fuzzy sets for the two inputs and a seven–membership function fuzzy set for the output.

    The offset input is named X (deviation between part and box) and the offset rate of change input is named DeltaX (rate of change of deviation). The fuzzy set for the output is named S (speed), which corresponds to the motor speed of conveyor B. The range of each fuzzy input and output variable is from 0 to 4095 counts. This corresponds to a range of ±24 inches for the deviation between the part and box positions, a range of ±10 inches/second for the rate of change of the offset, and a range of ±10 inches/second for the speed of the box conveyor.
    The fuzzy logic database for this system contains 25 rules. Figure 11 shows a matrix of the rules, describing the desired output according to the deviation between the part and the box and the rate of change of deviation. This matrix includes a description of the rule inputs and outputs, as well as their respective membership function labels. Once the fuzzy controller receives the inputs, it will determine the final output value based on a logical addition of the selected outcomes.

    PLCs and Fuzzy Logic (7)

    December 29, 2008
    FUZZY LOGIC APPLICATION EXAMPLE

    Fuzzy logic can be applied to a wide array of applications and industries, given that the application requires reasoned output values derived from system inputs or feedback.

    Figure 10 shows an example of a typical fuzzy logic application, a two-conveyor packaging system. The objective of this application is to synchronize two conveyors so that parts and packaging boxes are positioned correctly, regardless of the part and packaging box positions and the speed of conveyor.

    System Description and Operation
    In the system, the parts travel on conveyor A, pass onto the connecting conveyor, and then go to
    conveyor B, where they are boxed before going to the wrapping machine. The photoelectric sensors PE1 and PE2 detect the presence of a part and initiate a count to determine the part’s position from encoder 1. PE3 and PE4 detect the presence of a box and determine its position based on the count inputs from encoder 2.
    The control objective is to adjust the speed of conveyor B so that the packaging boxes arrive at the same time as the parts, meaning that they meet at the connecting conveyor. The process information required to implement this control is:
    • the offset between the part and the packaging box
    • the rate of change of the offset

    The parts on conveyor A travel at random intervals, but they travel at a constant speed. The boxes on conveyor B occur at regular intervals, and the speed of conveyor B can be controlled. The photoelectric sensors will be used in the PLC program to detect when to start timing and computing the data from the encoders. The two fuzzy input variables are the part/box offset and the rate of change of the offset.
    If a box is present at PE3 and a part is present at PE1, conveyor B should run at the same speed as conveyor A (the reference speed set initially by the operator). If the box is at PE3 but the part is behind PE1, the system will slow conveyor B until the part is at PE1. At this time, the fuzzy controller will indicate an increase in the speed of conveyor B so that it will catch up with conveyor A. The distance traveled by the box is calculated, using the input data from encoder 2, as the difference between the time the box passes PE3 and the time the part passes PE1. The difference in counts between encoder 1 and encoder 2 provides the part/box offset data. This value, denoted as X, is calculated as:

    X = (Encoder 1 counts) – (Encoder 2 counts)

    The rate of change of the offset is calculated as the difference between the current offset reading n) and the previous one (X(n–1)):

    to be continued…………….

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    PLCs and Fuzzy Logic (6)

    December 29, 2008
    Defuzzification
    The final output value from the fuzzy controller depends on the defuzzification method used to compute the outcome values corresponding to each label. The defuzzification process examines all of the rule outcomes after they have been logically added and then computes a value that will be the final output of the fuzzy controller. The PLC then sends this value to the output module. Thus, during defuzzification, the controller converts the fuzzy output into a real-life data value (e.g., 1720 counts).

    There are many defuzzification methods, but all are based on mathematical algorithms. The two most common defuzzification methods are:
    • maximum value
    • center of gravity

    Maximum Value Method.
    The maximum value defuzzification method bases the final fuzzy output value on the rule output with the highest membership function grade. This method is mainly used with discrete output membership functions. Referring to the chart in Figure 9, the maximum value defuzzification method would specify that the output value of 2048 counts be chosen as the final output value because it has the largest grade value. If two or more outcomes from two or more rules have the same grade level, then the controller will select the final outcome value based on criteria supplied by the user during the fuzzy system programming. Such criteria specifies choosing either the left-most or right-most grade value of the two equal labels and their corresponding number of counts. The left-most criteria selects the lowest output value (the one with the fewest counts), while the right-most criteria selects the highest output value (the one with the most counts). So if both ZR and PL in Figure 9 had output grade values of 0.6, a fuzzy controller using the left-most criteria would select the ZR output value (2048 counts). A controller using the right-most criteria would select the PL output (4095 counts).

    Center of Gravity Method.
    The center of gravity defuzzification method, also referred to as “calculating the centroid,” mathematically obtains the center of mass of the triggered output membership functions. In mathematical terms, a centroid is the point in a geometrical figure whose coordinates equal the average of all the other points comprising the figure. This point is the center of gravity of the figure. In simple terms, the center of gravity for a fuzzy output is the output data value (as shown on the X-axis), that divides the area under the fuzzy membership function curve into two
    equal parts. The center of gravity method is the most commonly used defuzzification method because it provides an accurate result based on the weighted values of several output membership functions. The output value that is sent to the output interface module is the output data value at the intersection of the horizontal axis and the centroid.
    The center of gravity method applies to noncontinuous output membership functions as well as
    continuous ones. In noncontinuous functions, the final output value for a seven-label output membership function (labels A through G) is expressed by the formula:

    This equation implies that the final value of the output will be equal to the sum of each rule outcome grade multiplied by its actual output data value (i.e., counts) divided by the sum of the rule outcome grades. Referring to the noncontinuous membership example in Figure 9, the fuzzy logic controller will decide to send an output of 2867 counts to the output interface after completing the center of gravity calculation, which is as follows:


    The fuzzy controller’s output is more than it would have been using the maximum value method (the maximum output label is ZR, which is 2048 counts). This indicates that the weighted value of the 0.4PL label pulls the value to the right (more counts).
    Fuzzy controllers that use continuous membership functions and the center of gravity defuzzification method also use the previous summation equation to approximate the centroid value. However, in this case, the controller uses approximate digitized values for each membership function to compute each of the points in the summation.