Flow Controller

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Flow Controller
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Pneumatic One Way Design Air Flow Control Valve RE-03
Pneumatic One Way Design Air Flow Control Valve RE-03
Paypal   US $9.19
Pneumatic Connector Flow Speed Control 4mm Tube Fitting
Pneumatic Connector Flow Speed Control 4mm Tube Fitting
Paypal   US $4.28
Pneumatic Flow Control Quick 90 Degree Fitting 6x9.5mm
Pneumatic Flow Control Quick 90 Degree Fitting 6x9.5mm
Paypal   US $2.74
MKS FRCA52163310 Delta Flow Ratio Controller, 500sccm
MKS FRCA52163310 Delta Flow Ratio Controller, 500sccm
Paypal   US $40.00
Lot of 2 Aro Flow Control Valves F03  3/8
Lot of 2 Aro Flow Control Valves F03 3/8" (4177)J
Paypal   US $29.99
BRAY 2IN BUTTERFLY FLOW CONTROL VALVE 178250 316 SS STAINLESS DISC 21/124IN AGCO
BRAY 2IN BUTTERFLY FLOW CONTROL VALVE 178250 316 SS STAINLESS DISC 21/124IN AGCO
Paypal   US $9.00
SMC AS2201F-01-08S FLOW CONTROL PNEUMATIC FITTING       BULK 10-PACK       NIB
SMC AS2201F-01-08S FLOW CONTROL PNEUMATIC FITTING BULK 10-PACK NIB
Paypal   US $29.99
2 New R410a Manifold-Port Flow Control Adapters+Hand Valve 1/4X5/16FFL HVAC Tool
2 New R410a Manifold-Port Flow Control Adapters+Hand Valve 1/4X5/16FFL HVAC Tool
Paypal   US $24.97
SMC AS2201F-01-08S FLOW CONTROL PNEUMATIC FITTING       BULK 10-PACK       NIB
SMC AS2201F-01-08S FLOW CONTROL PNEUMATIC FITTING BULK 10-PACK NIB
Paypal   US $29.99
DELTROL F35B 3/4IN PNEU-TROL BRASS FLOW CONTROL VALVE 3/4NPT 54633
DELTROL F35B 3/4IN PNEU-TROL BRASS FLOW CONTROL VALVE 3/4NPT 54633
Paypal   US $9.00
Sierra Instruments 902C Controller & 2 840D Side-Trak Analog Mass Flow Meters
Sierra Instruments 902C Controller & 2 840D Side-Trak Analog Mass Flow Meters
Paypal   US $455.00
HVAC Manifold/Tool/Port Adapter+Hand Valve Refrigerant Flow Control1/4X1/4 29980
HVAC Manifold/Tool/Port Adapter+Hand Valve Refrigerant Flow Control1/4X1/4 29980
Paypal   US $24.99
Parker N800S Carbon Steel Flow Control Needle Valve 1/2
Parker N800S Carbon Steel Flow Control Needle Valve 1/2" 5000 PSI 345 Bar Max
Paypal   US $13.01
Manifold-Port Adapter+Hand Valve Refrigerant Flow Control 5/16X1/4
Manifold-Port Adapter+Hand Valve Refrigerant Flow Control 5/16X1/4"FFL HVAC Tool
Paypal   US $24.99
CCS Custom Control Dual Snap 6255F 52S Flow Switch 8.25-6.75 GPM Flowswitch
CCS Custom Control Dual Snap 6255F 52S Flow Switch 8.25-6.75 GPM Flowswitch
Paypal   US $9.95
4mm Diameter Tube Threaded Pneumatic Air Flow Speed Controller
4mm Diameter Tube Threaded Pneumatic Air Flow Speed Controller
Paypal   US $5.96
MKS 2179A12CR1BV Mass Flow Controller MFC N2 100 SCCM
MKS 2179A12CR1BV Mass Flow Controller MFC N2 100 SCCM
Paypal   US $90.00
Manifold Flow Control Isolate Valve Adapter 1/4
Manifold Flow Control Isolate Valve Adapter 1/4"29980 Straight HVAC Service Tool
Paypal   US $24.99
Pneumatic Air Flow Speed Controller Black Silver Tone for 6mm Dia Tube
Pneumatic Air Flow Speed Controller Black Silver Tone for 6mm Dia Tube
Paypal   US $5.03
Vickers SystemStak Hydraulic Flow Control DGMFN-5-Y-A2W-B2W-30
Vickers SystemStak Hydraulic Flow Control DGMFN-5-Y-A2W-B2W-30
Paypal   US $49.99
2 New R410a Manifold-Port Flow Control Adapters+Hand Valve 1/4X5/16FFL HVAC Tool
2 New R410a Manifold-Port Flow Control Adapters+Hand Valve 1/4X5/16FFL HVAC Tool
Paypal   US $24.97
LOT 3x PISCO JAPAN PC12-03 FITTINGS & FLOW CONTROL PUSH-IN PNEUMATIC FITTINGS
LOT 3x PISCO JAPAN PC12-03 FITTINGS & FLOW CONTROL PUSH-IN PNEUMATIC FITTINGS
Paypal   US $.99
TYLAN UFC-1160A MASS FLOW CONTROLLER WF6 100 SCCM WITH CERTIFICATE OF COMPLIANCE
TYLAN UFC-1160A MASS FLOW CONTROLLER WF6 100 SCCM WITH CERTIFICATE OF COMPLIANCE
Paypal   US $250.00
TYLAN FC-260 MASS FLOW CONTROLLER 150 PSI WITH CERTIFICATE OF COMPLIANCE
TYLAN FC-260 MASS FLOW CONTROLLER 150 PSI WITH CERTIFICATE OF COMPLIANCE
Paypal   US $99.95
2 PNEU-TROL FCV-B FLOW CONTROL VALVE SPEED 1/4NPT BRASS NEEDLE CHECK VALVE 40446
2 PNEU-TROL FCV-B FLOW CONTROL VALVE SPEED 1/4NPT BRASS NEEDLE CHECK VALVE 40446
Paypal   US $3.00
NEW DELTROL FLUID F25B PNEU-TROL FLOW CONTROL VALVE 3/8IN NPT BRASS 55059
NEW DELTROL FLUID F25B PNEU-TROL FLOW CONTROL VALVE 3/8IN NPT BRASS 55059
Paypal   US $3.00
MKS FRCA52163310 Delta Flow Ratio Controller, 500sccm
MKS FRCA52163310 Delta Flow Ratio Controller, 500sccm
Paypal   US $40.00
Manifold-Port Adapter+Hand Valve Refrigerant Flow Control 5/16X1/4
Manifold-Port Adapter+Hand Valve Refrigerant Flow Control 5/16X1/4"FFL HVAC Tool
Paypal   US $24.99
VICKERS DIRECTIONAL HYDRAULIC FLOW CONTROL VALVE DGMFN-3-Y-A2W-B2W-41 10H
VICKERS DIRECTIONAL HYDRAULIC FLOW CONTROL VALVE DGMFN-3-Y-A2W-B2W-41 10H
Paypal   US $99.99
Unit Mass Flow Controller UFC-1500A NH3
Unit Mass Flow Controller UFC-1500A NH3
Paypal   US $125.00
1/2
1/2" IPS Dole Stainless Steel Domestic Cold Water Flow Control
Paypal   US $20.00
PARKER FLOW CONTROL PC M600S
PARKER FLOW CONTROL PC M600S
Paypal   US $80.00
Manifold Flow Control Isolate Valve Adapter 1/4
Manifold Flow Control Isolate Valve Adapter 1/4"29980 Straight HVAC Service Tool
Paypal   US $24.99
HVAC Manifold/Tool/Port Adapter+Hand Valve Refrigerant Flow Control1/4X1/4 29980
HVAC Manifold/Tool/Port Adapter+Hand Valve Refrigerant Flow Control1/4X1/4 29980
Paypal   US $24.99
SIGNET Flow Controller Control Panel  3-9000 Series
SIGNET Flow Controller Control Panel 3-9000 Series
Paypal   US $24.95
BINKS REGULATOR,GAUGE AND FLOW CONTROL VALVES    [PRE-OWNED]
BINKS REGULATOR,GAUGE AND FLOW CONTROL VALVES [PRE-OWNED]
Paypal   US $44.00
2 New R410a Manifold-Port Flow Control Adapters+Hand Valve 1/4X5/16FFL HVAC Tool
2 New R410a Manifold-Port Flow Control Adapters+Hand Valve 1/4X5/16FFL HVAC Tool
Paypal   US $24.97
HVAC Manifold/Tool/Port Adapter+Hand Valve Refrigerant Flow Control1/4X1/4 29980
HVAC Manifold/Tool/Port Adapter+Hand Valve Refrigerant Flow Control1/4X1/4 29980
Paypal   US $24.99
Lot of 6 Brooks Sho Rate 224-052 Gas Flow Rate Flow Meter Control Gage Gauge
Lot of 6 Brooks Sho Rate 224-052 Gas Flow Rate Flow Meter Control Gage Gauge
Paypal   US $.99
PFD Precision Flow Devides Model 914 4-Channel Flow Controller
PFD Precision Flow Devides Model 914 4-Channel Flow Controller
Paypal   US $79.95
MSA  FLOW CONTROL #459948  1.5 LITERS / MIN
MSA FLOW CONTROL #459948 1.5 LITERS / MIN
Paypal   US $15.00
Tylan Millipore 2900 mass flow controller mfc hi vacuum
Tylan Millipore 2900 mass flow controller mfc hi vacuum
Paypal   US $7.88
Aera FC 980C hi vacuum gas mass flow controller mfc
Aera FC 980C hi vacuum gas mass flow controller mfc
Paypal   US $7.88
Data Industrial mod # 2100 flow monitor controller as pictured
Data Industrial mod # 2100 flow monitor controller as pictured
Paypal   US $75.99
OMEGA Engineering 20+ Gas Selectible Mass Flow Controller
OMEGA Engineering 20+ Gas Selectible Mass Flow Controller
Paypal   US $599.00
OMEGA Engineering 20+ Gas Selectible Mass Flow Controller
OMEGA Engineering 20+ Gas Selectible Mass Flow Controller
Paypal   US $499.00
PARKER F1200 B BRASS FLOW CONTROL VALVE 3/4NPT 54812
PARKER F1200 B BRASS FLOW CONTROL VALVE 3/4NPT 54812
Paypal   US $11.00
Mass flow control Hastings Sensotec Transducer
Mass flow control Hastings Sensotec Transducer
Paypal   US $160.00
Hydrolux K-WE43P06C62C0BN/P15 Flow Control Valve HPN-706268
Hydrolux K-WE43P06C62C0BN/P15 Flow Control Valve HPN-706268
Paypal   US $39.99
DELTROL FLUID EDF-30-B EASY READ FLOW CONTROL VALVE FEMALE 3/4IN NPT BRASS 41608
DELTROL FLUID EDF-30-B EASY READ FLOW CONTROL VALVE FEMALE 3/4IN NPT BRASS 41608
Paypal   US $9.00
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Thermal gas mass flow controller, to 1 L/min Air / N<sub>2</sub>, Aluminum body w/ display Thermal gas mass flow controller, to 1 L/min Air / N2, Aluminum body w/ display
Sale Price: $882.00

These controllers feature an advanced straight-tube sensor that ensures accurate and repeatable results. Gas flow measurements are unaffected by moderate temperature and pressure variations at the inlet. The meter also allows a four-point calibration across the flow range to improve meter linearity. The flow rate set point can be established by either a local potentiometer or by a remote 4 to 20 mA or 0 to 5 VDC signal. Output data is sent via a 0 to 5 VDC or 4 to 20 mA signal; an analog-to-RS converter is also available for data collection and analysis on your PC. All controllers include a detachable 31/2-digit LCD that can be tilted up to 90° for easy reading. The display is remote mountable to three feet using extension cable 32662-70. The totalizer option 32650-70 will display total accumulated flow. The controller is protected from polarity reversal or short circuit by a built-in resettable fuse. Aluminum models have wetted materials of anodized aluminum, brass, and Viton®; stainless steel (SS) models have wetted materials of SS and Viton.Power supply is required - order at right Accuracy These precalibrated flow controllers operate at inlet pressures between 5 and 60 psi and at gas temperatures between 59 and 77°F (15 to 25°C) while maintaining the stated percent full-scale accuracy and linearity. When operating beyond 5 to 60 psi, add ±0.01%/psi full-scale; if operating beyond 59 to 77°F (15 to 25°C), add ±0.15%/°C full-scale. VITON-Reg TM DuPont Dow Elastometers L.L.C.

Flow controller, mass, differential pressure, for gas, 5 to 500 ml/min Flow controller, mass, differential pressure, for gas, 5 to 500 ml/min
Sale Price: $1,307.00

These meters measure flow via pressure drop across a laminar flow element (LFE). Because the flow element makes the flow stream laminar, placement in the process does not require straight pipe runs upstream or downstream of the meter, greatly simplifying installation. The LFEs also provide an outstanding turndown ratio of 100:1 giving the meter a very broad and accurate measuring range. As compared to thermal mass technologies, the LFE design provides an ultrafast response at start-up or input change, often within 20 milliseconds; there is also no thermal drift with this technology. An integrated keypad around the display is all that is required to program the unit for service-no additional costs for programming modules. The 0 to 5 VDC output allows transmission of the flow value to a remote display, recorder, or controller regulating a valve or pump. For portable flow metering applications, order the battery pack listed below. Units can be mounted via threaded taps in the meter body. Flowmeters include the integrated sensor, display, and transmitter. All models include a 120 VAC power adapter; 220 VAC European adapters. Meters feature dynamic display that simultaneously shows flow rate, line pressure, fluid temperature. For the unit shown, both power and input/output signals are transmitted through a single multi-pin connector.

Thermal gas mass flow controller, to 200 sccm Air / N<sub>2</sub>, Aluminum body w/ display Thermal gas mass flow controller, to 200 sccm Air / N2, Aluminum body w/ display
Sale Price: $882.00

These controllers feature an advanced straight-tube sensor that ensures accurate and repeatable results. Gas flow measurements are unaffected by moderate temperature and pressure variations at the inlet. The meter also allows a four-point calibration across the flow range to improve meter linearity. The flow rate set point can be established by either a local potentiometer or by a remote 4 to 20 mA or 0 to 5 VDC signal. Output data is sent via a 0 to 5 VDC or 4 to 20 mA signal; an analog-to-RS converter is also available for data collection and analysis on your PC. All controllers include a detachable 31/2-digit LCD that can be tilted up to 90° for easy reading. The display is remote mountable to three feet using extension cable 32662-70. The totalizer option 32650-70 will display total accumulated flow. The controller is protected from polarity reversal or short circuit by a built-in resettable fuse. Aluminum models have wetted materials of anodized aluminum, brass, and Viton®; stainless steel (SS) models have wetted materials of SS and Viton.Power supply is required - order at right Accuracy These precalibrated flow controllers operate at inlet pressures between 5 and 60 psi and at gas temperatures between 59 and 77°F (15 to 25°C) while maintaining the stated percent full-scale accuracy and linearity. When operating beyond 5 to 60 psi, add ±0.01%/psi full-scale; if operating beyond 59 to 77°F (15 to 25°C), add ±0.15%/°C full-scale. VITON-Reg TM DuPont Dow Elastometers L.L.C.

Flow controller, mass, differential pressure, for gas, 0.1 to 10 L/min Flow controller, mass, differential pressure, for gas, 0.1 to 10 L/min
Sale Price: $1,307.00

These meters measure flow via pressure drop across a laminar flow element (LFE). Because the flow element makes the flow stream laminar, placement in the process does not require straight pipe runs upstream or downstream of the meter, greatly simplifying installation. The LFEs also provide an outstanding turndown ratio of 100:1 giving the meter a very broad and accurate measuring range. As compared to thermal mass technologies, the LFE design provides an ultrafast response at start-up or input change, often within 20 milliseconds; there is also no thermal drift with this technology. An integrated keypad around the display is all that is required to program the unit for service-no additional costs for programming modules. The 0 to 5 VDC output allows transmission of the flow value to a remote display, recorder, or controller regulating a valve or pump. For portable flow metering applications, order the battery pack listed below. Units can be mounted via threaded taps in the meter body. Flowmeters include the integrated sensor, display, and transmitter. All models include a 120 VAC power adapter; 220 VAC European adapters. Meters feature dynamic display that simultaneously shows flow rate, line pressure, fluid temperature. For the unit shown, both power and input/output signals are transmitted through a single multi-pin connector.

Thermal gas mass flow controller, to 5 L/min Air / N<sub>2</sub>, Aluminum body w/ display Thermal gas mass flow controller, to 5 L/min Air / N2, Aluminum body w/ display
Sale Price: $882.00

These controllers feature an advanced straight-tube sensor that ensures accurate and repeatable results. Gas flow measurements are unaffected by moderate temperature and pressure variations at the inlet. The meter also allows a four-point calibration across the flow range to improve meter linearity. The flow rate set point can be established by either a local potentiometer or by a remote 4 to 20 mA or 0 to 5 VDC signal. Output data is sent via a 0 to 5 VDC or 4 to 20 mA signal; an analog-to-RS converter is also available for data collection and analysis on your PC. All controllers include a detachable 31/2-digit LCD that can be tilted up to 90° for easy reading. The display is remote mountable to three feet using extension cable 32662-70. The totalizer option 32650-70 will display total accumulated flow. The controller is protected from polarity reversal or short circuit by a built-in resettable fuse. Aluminum models have wetted materials of anodized aluminum, brass, and Viton®; stainless steel (SS) models have wetted materials of SS and Viton.Power supply is required - order at right Accuracy These precalibrated flow controllers operate at inlet pressures between 5 and 60 psi and at gas temperatures between 59 and 77°F (15 to 25°C) while maintaining the stated percent full-scale accuracy and linearity. When operating beyond 5 to 60 psi, add ±0.01%/psi full-scale; if operating beyond 59 to 77°F (15 to 25°C), add ±0.15%/°C full-scale. VITON-Reg TM DuPont Dow Elastometers L.L.C.

Thermal gas mass flow controller, to 500 sccm Air / N<sub>2</sub>, Aluminum body w/ display Thermal gas mass flow controller, to 500 sccm Air / N2, Aluminum body w/ display
Sale Price: $882.00

These controllers feature an advanced straight-tube sensor that ensures accurate and repeatable results. Gas flow measurements are unaffected by moderate temperature and pressure variations at the inlet. The meter also allows a four-point calibration across the flow range to improve meter linearity. The flow rate set point can be established by either a local potentiometer or by a remote 4 to 20 mA or 0 to 5 VDC signal. Output data is sent via a 0 to 5 VDC or 4 to 20 mA signal; an analog-to-RS converter is also available for data collection and analysis on your PC. All controllers include a detachable 31/2-digit LCD that can be tilted up to 90° for easy reading. The display is remote mountable to three feet using extension cable 32662-70. The totalizer option 32650-70 will display total accumulated flow. The controller is protected from polarity reversal or short circuit by a built-in resettable fuse. Aluminum models have wetted materials of anodized aluminum, brass, and Viton®; stainless steel (SS) models have wetted materials of SS and Viton.Power supply is required - order at right Accuracy These precalibrated flow controllers operate at inlet pressures between 5 and 60 psi and at gas temperatures between 59 and 77°F (15 to 25°C) while maintaining the stated percent full-scale accuracy and linearity. When operating beyond 5 to 60 psi, add ±0.01%/psi full-scale; if operating beyond 59 to 77°F (15 to 25°C), add ±0.15%/°C full-scale. VITON-Reg TM DuPont Dow Elastometers L.L.C.

Scythe Kaze Server 5.25 Scythe Kaze Server 5.25" 4 Channel Fan Controller / Temp Display - Black (KS01-BK)
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Precious aluminum design: High-quality materials were used when producing the Kaze Server. The front consists of brushed aluminum and accentuates the illuminated LCD display in an optimal way


Here are some more information for Flow Controller:
Flow Controller

Who would you be if you weren't in charge, and if you weren't in control? Do you have the self-esteem it takes to risk looking foolish? Are you willing to "put it out there" in a big way and trust your teammates to catch you if you fall?

What would happen if you had to find a way to agree with the present moment? Would you have the courage to allow the flow and stop resisting "what is?" Are you willing to accept or even agree with others even when you don't fully understand their point of view?

Depending upon your role in your company, owner, president, employee, entrepreneur, you'll have a standard "seminar answer." If you're on the top rung of the ladder you'll say something like "I've been to Covey's Seven Habits Training." If you are on the middle rung you'll say something like, "I teach this stuff and have developed the material." Or if you're on the bottom rung you'll say you've been through the "ropes course" at the company retreat.

Although these courses and methods are valuable, if you want to know the skinny on these answers to these questions, take the eight-week course at the Skinny Improv. The Skinny Improv is a comedy troop in Springfield Missouri. The troop performs every Friday and Saturday night, and offers lessons to anyone who wants to learn the same skills to use in business or in life. If you have an improve troop in your area it is worth the personal investment. You'll learn a lot about team building and even more about yourself. Here are some of the lessons I've learned after six weeks of investing in myself for the training.

Lesson One: It's not about you.

Although you are on the team, it's never really about you. It's about making everyone else look good. When you do your part and your intention is to be there for the other team members, then everyone is a star. It's not your job to get the limelight, to get the last word or deliver the funniest line. It's your job to make everyone else look good. When you focus on yourself, you do so at the expense of the team. In the business world being competent in lesson one will work magic for the team and work miracles for customer service.

Lesson Two: Go with the flow.

In Improv, you never know what the other person will do, so it's easy to get thrown off guard. When you are caught off guard, the natural response is to resist instead of looking for agreement. When you are used to being in control it's difficult to let go. If you are in a position of power you are used to planning and facilitating but you forget what it's like to participate. It's easy to ask others to step up but when you go with the flow you become a participant instead of the controller. So often in the business world we resist and stress over the current situations instead of looking for opportunities to go with the flow.

Lesson Three: Trust is paramount.

In order to have a great team you must trust that your team members are there for you. They will rescue you when you stumble, they will catch you when you fall. After all, they also believe in the philosophy that it's not about them, but it is about making you look good. What goes around comes around. The end result is a great customer experience and in Improv the audience is the customer. In the business world your end result is to satisfy the customer so that you can keep them. You do this by making sure the team supports each other so that they can deliver the end result.

Lesson Four: Judgment blocks success.

It's impossible to be creative in the midst of criticism. It doesn't matter if the criticism is directed toward someone else or yourself, judgment blocks the flow of energy. It takes discipline and practice to learn how to suspend the gremlins in your head that tell you how stupid you look and it takes a conscious positive intention to allow others the same courtesy.

Lesson Five: Growth takes courage.

In order to learn something new we have to be willing to leave our comfort zone momentarily and that takes the courage to risk. When you believe that everyone on your team has your best interests at heart, and that you will not be judged your capacity for courage is maximized. You can only risk when you have trust, when you have learned to go with the flow, you let go of judgment, and when you've been on the giving and receiving end of the philosophy that "it isn't about you."

Marlene Chism is an author, speaker and founder of The Stop Drama Methodology, an 8-part empowerment process to increase clarity, productivity, and personal effectiveness. Marlene works with leaders, owners and HR directors who want to run their office with no complaints, no excuse and no regrets. To see more go to http://www.stopyourdrama.com/Productivity.html or call 1.888.434.9085 to inquire about speaking.

Simulation and Mathematical Analysis of Optimal Power Flow in Power System

I. INTRODUCTION

T

HE optimal power flow has been frequently solved using classical optimization methods. The OPF has been usually considered as the minimization of an objective function representing the generation cost and/or the transmission loss. The constraints involved are the physical laws governing the power generation-transmission systems and the operating limitations of the equipment. Effective optimal power flow is limited by (i) the high dimensionality of power systems and (ii) the incomplete domain dependent knowledge of power system engineers. The first limitation is addressed by numerical optimization procedures based on successive linearization using the first and the second derivatives of objective functions and their constraints as the search directions or by linear programming solutions to imprecise models [1-4]. The advantages of such methods are in their mathematical underpinnings, but disadvantages exist also in the sensitivity to problem formulation, algorithm selection and usually converge to a local minimum [5]. The second limitation, incomplete

domain knowledge, precludes also the reliable use of expert systems where rule completeness is not possible.Genetic algorithms offer a new and powerful approach to these optimization problems made possible by the increasing availability of high performance computers at relatively low costs. These algorithms have recently found extensive applications in solving global optimization searching problems when the closed-form optimization technique cannot be applied. Genetic algorithms (GAs) are parallel and global search techniques that emulate natural genetic operators. The GA is more likely to converge toward the global solution because it, simultaneously, evaluates many points in the parameter space. It does not need to assume that the search space is differentiable or continuous [6] in recent paper [7], the Genetic Algorithm

Optimal Power Flow (GAOPF) problem is solved based on the use of a genetic algorithm load flow, and to accelerate the concepts it propose the use of gradient information by the use of the steepest decent method. The method is not sensitive to the starting points and capable to determining the global optimum solution to the OPF for range of constraints and objective functions. But GAOPF requires two load flow to be performed per individual, per iteration because all controllable variables are included in the fitness. In this paper we develop a simple genetic algorithm applied to the problem of optimal power flow in large power distribution systems. To accelerate the processes of GAOPF, the controllable variables are decomposed to active constraints that effect directly the cost function are included in the Genetic algorithms process and passive constraints which are updating using a conventional load flow program, only, one time after the convergence on the GAOPF.

In which the search of the optimal parameters set is performed using into the account that the power losses are 2% of the power demand. The slack bus parameter would be recalculated in the load flow process to take the effect of the passive constraints.

II. PROBLEM FORMULATION

The standard OPF problem can be written in the following form,

Minimize F(x) (the objective function)

Subject to:

hi(x) = 0, i = 1, 2, ..., n (equality constraints)

gj(x) = 0, j = 1, 2, ...,m (inequality constraints)

Where x is the vector of the control variables that is those which can be varied by a control center operator (generated active and reactive powers, generation bus voltage magnitudes, transformers taps etc.);

The essence of the optimal power flow problem resides in reducing the objective function and simultaneously satisfying the load flow equations (equality constraints) without violating the inequality constraints

A. Objective Function

The most commonly used objective in the OPF problem formulation is the minimization of the total cost of real power generation. The individual costs of each generating unit are assumed to be function, only, of active power generation and are represented by quadratic curves of second order. The objective function for the entire power system can then be written as the sum of the quadratic cost model at each generator.

(1)

where ng is the number of generation including the slack bus. Pgi is the generated active power at bus i. ai, bi and ci are the unit costs curve for ith generator.

B. Types of equality constraints

While minimizing the cost function, it’s necessary to make sure that the generation still supplies the load demands plus losses in transmission lines. Usually the power flow equations are used as equality constraints.

(2)

Where active and reactive power injection at bus i are defined in the following equation:

(3)

C. Types of inequality constraints

The inequality constraints of the OPF reflect the limits on physical devices in the power system as well as the limits created to ensure system security. The most usual types of inequality constraints are upper bus voltage limits at generations and load buses, lower bus voltage limits at load buses, var. limits at generation buses, maximum active power limits corresponding to lower limits at some generators, maximum line loading limits and limits on tap setting of TCULs and phase shifter. The inequality constraints on the problem variables considered include:

• Upper and lower bounds on the active generations at generator buses Pgimin ?Pgi ? Pgimax , i = 1, ng.

• Upper and lower bounds on the reactive power generations at generator buses and reactive power injection at buses with VAR compensation Qgimin ? Qgi ? Qgimax, i = 1, npv

• Upper and lower bounds on the voltage magnitude at the all buses Vimin ? Vi ? Vimax , i = 1, nbus.

• Upper and lower bounds on the bus voltage phase angles: , i = 1, nbus.

It can be seen that the generalized objective function F is a non-linear, the number of the equality and inequality constraints increase with the size of the power distribution systems. Applications of a conventional optimization technique such as the gradient-based algorithms to a large power distribution system with a very non-linear objective functions and great number of constraints are not good enough to solve this problem. Because it depend on the existence of the first and the second derivatives of the objective function and on the well computing of these derivative in large search space.

III. GENETIC ALGORITHM IN OPTIMAL POWER FLOW

A. Description of Genetic Algorithms

The genetic algorithms are part of the evolutionary algorithms family, which are computational models, inspired in the Nature. Genetic algorithms are powerful stochastic search algorithms based on the mechanism of natural selection and natural genetics. GAs works with a population of binary string, searching many peaks in parallel. By employing genetic operators, they exchange information between the peaks, hence reducing the possibility of ending at a local optimum. GAs are more flexible than most search methods because they require only information concerning the quality of the solution produced by each parameter set (objective function values) and not lake many optimization methods which require derivative information, or worse yet, complete knowledge of the problem structure and parameters.

There are some difference between GAs and traditional searching algorithms [8][9]. They could be summarized as follows:

• The algorithms work with a population of string, searching many peaks in parallel, as opposed to a single point.

• GAs work directly with strings of characters representing the parameters set not the parameters themselves.

• GAs use probabilistic transition rules instead of deterministic rules.

• GAs use objective function information instead of derivatives or others auxiliary knowledge.

• GAs have the potential to find solutions in many different areas of the search space simultaneously.

B. Genetic Algorithm Applied to optimal power flow

A simple Genetic Algorithm is an iterative procedure, which maintains a constant size population P of candidate solutions. During each iteration step (generation) three genetic operators (reproduction, crossover, and mutation) are performing to generate new populations (offspring), and the chromosomes of the new populations are evaluated via the value of the fitness which is related to cost function. Based on these genetic operators and the evaluations, the better new populations of candidate solution are formed.

With the above description, a simple genetic algorithm is given as follow [6]:

1. Generate randomly a population of binary string

2. Calculate the fitness for each string in the population

3. Create offspring strings through reproduction, crossover and mutation operation.

4. Evaluate the new strings and calculate the fitness for each string (chromosome).

5. If the search goal is achieved, or an allowable generation is attained, return the best chromosome as the solution; otherwise go to step 3.

We now describe the details in employing the simple GA to solve the optimal power flow problem.

B.1 Chromosome coding and decoding

GAs works with a population of binary string, not the parameters themselves. For simplicity and convenience, binary coding is used in this paper. With the binary coding method, the active generation power set of 9-bus test system (Pg1,Pg2 and Pg3) would be coded as binary string of O’s and 1’ with length B1, B2, and B3 (may be different), respectively. Each parameter Pgi have upper bound Ui and lower bound Li .The choice of B1, B2, and B3 for the parameters is concerned with the resolution specified by the designer in the search space. In the binary coding method, the bit length Bi and the corresponding resolution

Ri is related by

(4)

As result, the Pgi set can be transformed into a binary string (chromosome) with length ÓBi and then the search space is explored. Note that each chromosome present one possible solution to the problem. For example, suppose the parameter domain of (Pg1,Pg2 and Pg3) which is presented in Table I:

TABLE. I. PARAMETER SET OF Pg1

Bus Pmin

(p.u) Pmax

(p.u) a

(S/hr) b

(S/MW.hr) c (S/MW2.hr)

1 0.30 1.8 105.0 2.45 0.0.1

2 0.15 0.9 44.1 3.51 0.01

3 0.40 1.9 40.6 3.89 0.01

If the resolution (R1, R2, R3) is specified as (0.1, 0.05, 0.1), from (3) we have (B1, B2, B3) = (4, 4, 4). Then the parameter set (Pg1, Pg2 and Pg3) can be coded according to the following (Table II):

TABLE .II. CODING OF Pgi PARAMETER SET

Pg1 Code Pg2 Code Pg3 Code

0.3 0000 0.15 0000 0.4 0000

0.4 0001 0.20 0001 0.5 0001

0.5 0010 0.30 0010 0.6 0010

0.6 0011 0.30 0011 0.7 0011

0.7 0100 0.35 0100 0.8 0100

0.8 0101 0.40 0101 0.9 0101

0.9 0110 0.45. 0110 1.0 0110

1.0 0111 0.50 0111 1.1 0111

1.1 1000 0.55 1000 1.2 1000

1.2 1001 0.60 1001 1.3 1001

1.3 1010 0.65 1010 1.4 1010

1.4 1011 0.70 1011 1.5 1011

1.5 1100 0.75 1100 1.6 1100

1.6 1101 0.80 1101 1.7 1101

1.7 1110 0.85 1110 1.8 1110

1.8 1111 0.90 1111 1.9 1111

If the candidate parameters set is (1.7, 0.30, 1.1), then the chromosome is a binary string 111000110111. The decoding procedure is the reverse procedure. The first step of any genetic algorithm is to generate the initial population. A binary string of length L is associated to each member (individual) of the population. The string is usually known as a chromosome and represents a solution of the problem. A sampling of this initial population creates an intermediate population. Thus, some operators (reproduction, crossover and mutation) are applied to this new intermediate population in order to obtain a new one.

Process, that starts from the present population and leads to the new population, is named a generation when executing a genetic algorithm (Table III).

TABLE. III. First generation of GA process for 9bus System

Chrom Initial population Pg1

(p.u) Pg2

(p.u) Pg3

(p.u) Fcost

(s/kwh)

1 000111111100 0.4 0.90 1.60 2102.0253

2 000100101011 0.4 0.30 1.50 2104.7070

3 101010011011 103 0.65 1.50 2101.2549

4 111001010111 107 0.45 1.10 2102.5335

Sum 8409.7502

Average 2102.4376

Max 2104.7070

B.2 Crossover

Crossover is the primary genetic operator, which promotes the exploration of new regions in the search space. For a pair of parents selected from the population the recombination operation divides two strings of bits into segments by setting a crossover point at random, i.e. Single Point Crossover. The segments of bits from the parents behind the crossover point are exchanged with each other to generate their offspring. The mixture is performed by choosing a point of the strings randomly, and switching their segments to the left of this point. The new strings belong to the next generation of possible solutions. The strings to be crossed are selected according to their scores using the roulette wheel [6]. Thus, the strings with larger scores have more chances to be mixed with other strings because all the copies in the roulette have the same probability to be selected.

B.3 Mutation

Mutation is a secondary operator and prevents the premature stopping of the algorithm in a local solution. The mutation operator is defined by a random bit value change in a chosen string with a low probability of such change. The mutation adds a random search character to the genetic algorithm, and it is necessary to avoid that, after some generations, all possible solutions were very similar ones.

All strings and bits have the same probability of mutation. For example, in the string 110011101101, if the mutation affects to time bit number six, the string obtained is 110011001101 and the value of Pg2 change from 0.85 p.u to 0.75 p.u.

B.4 Reproduction

Reproduction is based on the principle of survival of the better fitness. It is an operator that obtains a fixed number of copies of solutions according to their fitness value. If the score increases, then the number of copies increases too. A score value is of associated to a given solution according to its distance of the optimal solution (closer distances to the optimal solution mean higher scores).

B.5 Fitness of candidate solutions and cost function

The cost function is defined as:

Our objective is to search (Pg1, Pg2, and Pg3) in their admissible limits to achieve the optimization problem of OPF. The cost function F(x) takes a chromosome (a possible (Pg1, Pg2, Pg3) and returns a value. The value of the cost is then mapped into a fitness value Fit (Pg1, Pg2, and Pg3) so as to fit in the genetic algorithm. To minimize F(x) is equivalent to getting a maximum fitness value in the searching process.

(5)

A chromosome that has lower cost function should be assigned a larger fitness value. The objective of OPF has to be changed to the maximization of fitness to be used in the simulated roulette wheel as follows:

(6)

Fig. 1. A Simple flow chart of the GAOPF

The use of penalty functions in many OPF solutions techniques to handle generation bus reactive power limits can lead to convergence problem due to the distortion of the solution surface. In this method no penalty functions are required. Because only the active power of generators are used in the fitness. And the reactive levels are scheduled in the load flow process. Because his essence of this idea is that the constraints are partitioned in two types of constraints, active constraints are checked using the GA procedure and the reactive constraints are updating using an efficient Newton-Raphson Load flow procedure.

C. Load Flow calculation

After the search goal is achieved, or an allowable generation is attained by the genetic algorithm. It’s required to performing a load flow solution in order to make fine adjustments on the optimum values obtained from the GAOPF procedure. This will provide updated voltages, angles and transformer taps and points out generators having exceeded reactive limits. to determining all reactive power of all generators and to determine active power that it should be given by the slack generator using into account the deferent reactive constraints. Examples of reactive constraints are the min and the max reactive rate of the generators buses and the min and max of the voltage levels of all buses. All these require a fast and robust load flow program with best convergence properties.

The developed load flow process is based upon the full Newton-Raphson algorithm using the optimal multiplier technique [10][11].

IV. APPLICATION STUDY

The GAOPF has been developed by the use of Borland C++ Builder version 5. It is tested using the modified IEEE 30-bus system [12]. The system consists of 41 lines, 6 generators, 4 Tap-changing transformers, and shunt capacitor banks located at 9 buses (Figure 2). The parameter settings to execute GAOPF are probability of crossover = 0.5, probability of mutation = 0.7, the population size is 48, the power mismatch tolerance is 0.0001 p.u and other parameters are presented in (Table IV).

TABLE IV. POWER GENERATION LIMITS AND GENERATOR COST PARAMETERS OF IEEE 30-BUS SYSTEM IN P.U (SB=100MVA)*

Bus Pmin Pmax Qmin Qmax Vmin Vmax a b c.10-2

1 0.50 2.00 0.20 2.00 0.95 1.10 0 200 037.5

2 0.20 0.80 0.20 1.00 0.95 1.10 0 175 175.0

5 0.15 0.50 0.15 0.80 0.95 1.10 0 100 625.0

8 0.10 0.35 0.15 0.60 0.95 1.10 0 325 083.0

11 0.10 0.30 0.10 0.50 0.95 1.10 0 300 250.0

13 0.12 0.40 0.15 0.60 0.95 1.10 0 300 250.0

Fig. 2. IEEE 30-bus electrical system topology

To compare these results with conventional method using the same cost objective function we have take conventional method present in [13]. The method is based on a Quasi-Newton Method using Broyden-Fletcher-Goldfarb-Shanno (BFGS) updating formula and iterated with the Newton Raphson load flow. The resulting cost and power losses are presented in (Table.V).The result show that the method presented gives much better results than the other method. The difference in generation cost between these two studies (803.699 $/kW?hr compared to 807,782 $/kW?hr) and in Real power loss (9.5177 MW compared to 8.805 MW) clearly shows the advantage of this method. In addition, it is important to point out that this simple genetic algorithm OPF converge in an acceptable time. For this test system was approximately 7 seconds, and it converged to highly optimal solutions set after 20 generations tested with Pentium I, 166 MHZ, 32MO. The optimum active power is in their secure values and is far from the min and max limits. It is also clear from the optimum solution that the GA easily prevent the violation of all the active constraints. The security constraints are also checked for voltage magnitudes and angles (Figure 3). The voltage magnitudes and the angles are between their minimum and the maximum values. No load bus was at the lower limit of the voltage magnitudes (0.9 p.u).

The proposed GAOPF is also compared with the evolutionary methods of references [7,8]. The results including the generation cost, real power losses and convergence time compared with published evolutionary methods are shown in Table .VI.

The results are similar to those obtained with the published evolutionary programming based OPF program and using the same cost objective function. It is also important to point out that the computing time of this GAOPF compared with that of the published evolutionary methods is better by more than a 9:1 speed ratio.

Fig.3 Voltage levels of IEEE 30 Bus electrical Network

TABLE . V. RESULTS OF GAOPF COMPARED WITH

IEEE 30-BUS SYSTEM

Variable Lower Upper Initial state Classical OPF GAOPF

P1(MW) 50 200 99.211 170.237 179.367

P2(MW) 20 80 80.00 44.947 44.24

P5(MW) 15 50 50.00 28.903 24.61

P9(MW) 10 35 20.00 17.474 19.90

P11(MW) 10 30 20.00 12.174 10.71

P13(MW) 12 40 20.00 18.468 14.09

Q1(MVAR) -20 200 5.335 -4.886 -30156

Q2(MVAR) -20 100 27.687 34.333 42.543

Q5(MVAR) -15 50 21.544 21.945 26.292

Q9(MVAR) -15 60 22.933 17.740 22.768

Q11(MVAR) -10 50 38.883 29.580 29.923

Q13(MVAR) -15 60 40.345 31.460 32.346

?1(deg) -14.0 0.00 0.00 0.000 0.000

?2(deg) -14.0 0.00 -1.77 -3.463 -3.674

?5(deg) -14.0 0.00 -6.50 -9.597 -10.14

?8(deg) -14.0 0.00 -5.64 -7.741 -10.00

?11(deg) -14.0 0.00 -4.66 -8.167 -8.851

?13(deg) -14.0 0.00 -7.24 -9.064 -10.13

Generation cost (S/KW.hr)

Real power loss(MW) 901.918 807.782 803.699

5.812 8.805 9.5177

TABLE. VI. RESULTS OF GAOPF COMPARED WITH EVOLUTIONARY METHODS

Variable GAOPF EPOPF

P1(MW)

P2(MW)

P5(MW)

P8(MW)

P11(MW)

P18(MW) 178.0875

48.722

21.454

20.955

11.768

12.052 173.8262

49.998

21.386

22.63

12.928

12.00

Generation cost (S/hr) 802.4484 802.5557

Real power loss (MW) 9.6372 9.3683

Time(sec) 315 51.4

V . CONCLUSION

Application of Genetic approach to Optimal Power Flow has been explored and tested. A simulation results show that a simple genetic algorithm can give a best result using only simple genetic operations such as proportionate reproduction, simple mutation, and one-point crossover in binary codes. It’s recommended to indicate that in large-scale system the numbers of constraints are very large consequently the GA accomplished in a large CPU time.

To save an important CPU time, the constraints are to be decomposing in active constraints and reactive ones. The active constraints are the parameters whose enter directly in the cost function and the reactive constraints are infecting the cost function indirectly. With this approach, only the active constraints are taken to calculate the optimal solution set. And the reactive constraints are taking in an efficient load flow by recalculate active power of the slack bus. The developed system was then tested and validated on the IEEE30-bus system. Solutions obtained with the developed Genetic Algorithm Optimal Power Flow program has shown to be almost as fast as the solutions given by a conventional language. Our GAOPF appears to be faster than other published GAOPF methods.

VI . REFERENCES

[1] H. W. Dommel, W. F. Tinney, Optimal Power Flow Solutions, IEEE Transactions on power apparatus and systems, Vol. PAS-87, No. 10, p. 1866-1876, October 1968.

[2] K. Y. Lee, Y.M. Park, and J.L. Ortiz, A United Approach to Optimal Real and Reactive Power Dispatch, IEEE Transactions on Power Systems, Vol. PAS-104, p. 1147-1153, May 1985.

[3] M. Sasson, Non linear Programming Solutions for load flow, minimum loss, and economic dispatching problems, IEEE Trans. on power apparatus and systems, Vol. PAS-88, No. 4, April 1969.

[4] T. Bouktir, M. Belkacemi, K. Zehar, Optimal power flow using modified gradient method, Proceeding ICEL’2000, U.S.T.Oran, Algeria, Vol. 2, p. 436-442, 13-15 November 2000.

[5] R. Fletcher, Practical Methods of Optimisation, John Willey & Sons, 1986.

[6] D. E. Goldberg Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley Publishing Company, Ind. USA, 1989.

[7] J. Yuryevich, K. P. Wong, Evolutionary Programming Based Optimal Power Flow Algorithm, IEEE Transaction on power Systems, Vol. 14, No. 4, November 1999.

[8] L.L. Lai, J. T. Ma, R. Yokoma, M. Zhao Improved genetic algorithms for optimal power flow under both normal and contingent operation states, Electrical Power & Energy System, Vol. 19, No. 5, p. 287-292, 1997.

[9] B. S. Chen, Y. M. Cheng, C. H. Lee, A Genetic Approach to Mixed H2/H00 Optimal PID Control, IEEE Control system, p. 551-59, October 1995.

[10] Glenn W. Stagg, Ahmed H. El Abiad, Computer methods in power systems analysis, Mc Graw Hill international Book Campany, 1968.

[11] S. Kumar, R. Billinton, Low bus voltage and ill-conditioned network situation in a composite system adequacy evaluation, IEEE transactions on power systems, vol. PWRS-2, No. 3, August 1987.

[12] L. Terra, M. Short, Security constrained reactive power dispatch, IEEE transaction on power systems, Vol. 6, No. 1, February 1991.

[13] T. Bouktir , M. Belkacemi , L. Benfarhi and A. Gherbi, Oriented Object Optimal Power Flow, the UPEC 2000, 35th Universities Power Engineering Conferences Belfast, Northern Ireland, 6-8 September 2000.

About the Author

Assistant professor in lord venkateswara engineering college.I am doing phd in sathyabama university, Tamil Nadu,India.

what is better for air flow-a throttle body or 4 barrel carburetor?

this is talking specifically as the throttle plate (fuel would be distributed at the port & controller via a standalone controller), my question is:

as far as efficiency goes, is it better to have one big round throttle plate, or separate smaller round throttle plates-highly tuned for the application, which open one at a time allowing perfectly metered airflow with possibly less restriction & more efficiency.

is this correct or incorrect and why?

First off, a throttle body doesn't need a venturi - which is essentially a restriction to the air flow.
As far as "highly tuned" - the air flow into an engine is always a compromise, for both power and efficiency - that's why vehicle manufactures are often using duel runner intakes (12 runners on a V6, for instance) to better control the air flow at both high and low rpm's.

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