ADVANCED THERMAL MOTOR PROTECTION USING DIGITAL RELAYS

Transcription

1 ADVANCED THEMAL MOTO POTECTION USING DIGITAL ELAYS Ed Lebenhaft, P.E. Calpine Corporation Mark Zeller Schweitzer Engineering Laboratories, Inc. ABSTACT The era of protecting rotating equipment using electromechanical devices has faded away. Today s motor protection is accomplished wi digital protective relays. Digital relays are multiphase, multifunction units at offer not only protection but also alarming, historical operational data, and communication to oer microprocessor-based devices in a plant. The most important facet in motor protection is e ability to accurately replicate heat flow into and out of a motor. This paper discusses e dual first order ermal model and its superior ability to protect ac motors from overtemperature conditions during starting and running states. INTODUCTION Digital relays are multiphase, multifunction microprocessor-based devices. Wi proper mechanical and electrical design precautions, ese relays offer highly reliable and advanced protection of power system components. Any past protection limitations experienced in e world of electromechanical relays are no longer a factor. If a situation can be maematically described, e microprocessor in a digital relay can be programmed to tackle at problem. Because of e immense computing power of today s microprocessors, digital relays offer additional, highly important features to complement protection. They alarm, store historical operating data about e protected equipment and e power system it is connected to, and communicate to oer microprocessors in e plant, using a large selection of communications protocols. Digital relays are also miniature programmable logic controllers (PLCs). elay protective elements, digital inputs, digital outputs, and analog quantities can be used in logic statements, generating custom control schemes to suit specific applications. Digital relays are no longer standalone protective devices. They can be incorporated into e overall manufacturing process in a plant. The world of motor protection presents unique challenges. The most prominent challenge is modeling of motor temperature based on electrical current flow. This paper discusses e dual first order ermal model, which is based on e ermodynamic laws of heat flow. OVEVIEW OF THE FIST ODE THEMAL MODEL FIGUE illustrates e first order ermal model. The major components of e model are: Heat source. Heat flow from e source, I r, is measured in watts (W). Thermal capacitance, C, which represents a motor wi a ermal capacity to absorb heat from e heat source. The unit of ermal capacitance is W s/ C. Thermal resistance,, which represents e heat dissipated by a motor to its surroundings. The unit of ermal resistance is C/W.

2 Temperature, U. The unit of temperature is C. Comparator, which compares e calculated motor temperature wi a pre-set value based on e motor manufacturer s data. U trip U + _ TIP Heat Source I r ( I + r I r) C Motor Heat Dissipation FIGUE. First Order Thermal Model The qualitative analysis of is model states at heat produced by e heat source is transferred to e motor, which in turn dissipates e heat to e surrounding environment. The quantitative analysis is defined by a first order linear differential equation, similar to a parallel resistorcapacitor (C) electrical circuit: where: I r = total heat flow (W) du C = heat flow into motor (W) dt U = heat flow into surroundings (W) du U = + (W) () Ir C dt Motors comprise two major electrical components, stator and rotor. The stator produces a rotating magnetic field (at line frequency) in e air gap, inducing voltage in e rotor bars. This induced voltage produces current flow in e rotor bars. otor current produces a magnetic field of its own. The rotor magnetic field is at 9 degrees to e air-gap magnetic field, us generating torque tangential to e rotor surface, resulting in rotational force, us turning e shaft. Because e construction of e stator and rotor is dissimilar, so are eir ermal characteristics. To accommodate e difference in stator and rotor ermal properties, two separate ermal models are used to achieve greater accuracy: ) otor model a. Starting element protects e rotor during e starting sequence. b. unning element protects e rotor when e motor is up to speed and running. ) Stator model protects e stator during starting and running. Transition from one rotor element to e oer occurs at.5 times e rated full-load current of e motor.

3 APPLYING FIST ODE THEMAL MODEL TO MOTO STATING Starting an ac motor is considered an adiabatic (lossless) process. Starting deposits a large amount of heat (magnitudes greater an rated heating) in e rotor bars. Also, e duration of e starting sequence is magnitudes shorter an motor ermal time constants. Thus, it is regarded at any heat deposited in e rotor will not dissipate to e surroundings during e starting sequence. It will dissipate later when e motor is up to speed and running, and air flows in e air gap. Applying is assumption to e first order ermal model depicted in FIGUE, we are effectively stating at e ermal resistance of e rotor during starting is infinity ( = ). Substituting is condition into () yields: du U du I r = C + = C dt dt (W) () earranging (): I r du = dt ( C) C The ermal capacity of a motor is a physical attribute and does not change. Motor resistance is assumed to be constant at is point. Convert e above expression to per-unit (pu) quantity by substituting e following: Thus: Integrating e expression: The solution to is general integral is: r = C = pu du = I dt = = du I dt I dt Motor manufacturers supply ermal limit information as part of motor data. U = I t (pu C) (3) The starting ermal limit is expressed in terms of e maximum time (motor safe stall time) at corresponding locked-rotor current can be applied to a motor. Applying is to (3): I = I LA (pu locked rotor, amperes) t = T STALL (safe stall time, seconds) trip LA STALL U = I T (pu C) (4) 3

4 Incorporating e above into FIGUE results in a rotor I t starting element in FIGUE. I LA T STALL U + _ TIP Heat Source I C = FIGUE. otor I t Starting Element Plotting e pu temperature response of is model versus e line current of e motor, e response curve is a straight line, as illustrated in FIGUE 3. Temperature (U/UL), otor Current = M Motor Torque Motor Current otor Temperature Constant Seconds FIGUE 3. otor I t Starting Element esponse Curve U This model keeps e rotor resistance constant at M, which occurs at standstill (S =.) and is considered pu. HIGH-INETIA STATING The rotor I t starting element performs well except for high-inertia starts. A high-inertia start is when e time to accelerate a motor to rated speed is equal to or longer an its specified safe stall time. When trying to use e I t starting element in high-inertia cases, e starting ermal limit of I LA T STALL is reached before e current drops below.5 FLA, resulting in premature tripping of e motor, as shown in FIGUE 3. This would occur during every start. In oer words, e motor cannot be started successfully. The solution is to use a speed switch. The reluctance of many customers to use speed switches led to e development of a rotor starting element at dispenses wi e use of a speed switch in a motor starting logic scheme, while providing reliable and accurate protection during is critical state. 4

5 INDUCTION MACHINE EQUIVALENT CICUIT At e dawn of e twentie century, an engineer and inventor named Charles Steinmetz created an equivalent circuit for induction machines. It is still e only equivalent circuit used today and is shown in FIGUE 4. S r ( S ) S FIGUE 4. Induction Machine Equivalent Circuit A closer look at e circuit reveals several interesting observations at might not be obvious at first glance: The stator and magnetizing branches are always connected across e supply voltage; us ey are exposed to line frequency at all times. The numerical value of stator impedance is fixed. The rotor branch is not connected to e line voltage. Instead, it is exposed to e voltage induced by e air-gap magnetic field. This voltage frequency depends on how quickly rotor bars cut e magnetic field. The numerical value of rotor impedance varies wi e induced voltage frequency. This frequency is e difference between e electrical frequency of e line voltage and e mechanical rotational speed of e rotor/shaft assembly. The difference is called slip, S. otor impedance is slip dependent. Magnetic flux (us current) distribution in e rotor bar varies wi rotor speed. At standstill, because of e intense air-gap magnetic field (function of e starting current), only a small portion of e rotor bar cross section conducts rotor current (FIGUE 5). At rated speed, most of e rotor bar cross section is used (FIGUE 5). This fact influences apparent rotor resistance, r. otor resistance at standstill is substantially larger an at rated speed. r is speed dependent, r (S). This particular phenomenon is e key ingredient at makes e slipdependent ermal model possible. Starting Slip = ated Slip = S Skin Effect Deep Bar Effect r Changes Wi otor Speed FIGUE 5. otor Bars Current Distribution 5

6 CALCULATING MOTO SLIP Let us calculate e input impedance of e induction machine equivalent circuit. After calculating and separating it into its real and imaginary components, e real part represents e input resistance of an induction machine. Motor input resistance,, is: where: S = stator resistance r (S) = rotor resistance S = motor slip A =. (empirical constant) (S) A S r = S + (pu Ω) (5) eference [] shows e detailed derivation of. It also derives e expression for r (S) in terms of maximum rotor resistance, M, which occurs at standstill (S = ), and normal rotor resistance, N, which occurs at rated motor speed (S = rated). The expression is: Substituting (6) into (5) and solving for S yields: (S) r = (M N) S+ N (pu Ω) (6) N S = A ( ) ( ) S M N (7) Two quantities are required by e slip-dependent ermal model in order to calculate fixed parameters S, M, and N : FLS = full-load slip LQ = locked-rotor torque (at S = ) When FLS and LQ are entered as set points, e algorim automatically calculates M and N and stores em in nonvolatile memory. The moment e motor is energized, e relay takes e first snapshot of motor input impedance, Z; extracts e real component, ; and calculates stator resistance, S. The equations for M, N, and S are: LQ = (pu Ω) (8) LA M Q S FLS = = = FLS (pu Ω) (9) ATED N IFLA = = (pu Ω) (). M S.833 M 6

7 Now, slip is solely a function of motor input resistance. Motor input resistance is measured and updated every four milliseconds. Slip is calculated every two line frequency cycles. A case study using,5 HP induction motor data illustrates e relationship between motor input resistance, motor slip, and rotor resistance. FIGUES 6, 7, and 8 clearly illustrate e close dependence of rotor resistance on motor slip at, in turn, is extracted from motor input resistance. Total (pu) FIGUE 6. Motor Input esistance During Starting Slip Seconds FIGUE 7. Motor Slip During Starting 7

8 .4. otor esistance r pu MODIFYING THE STATING ELEMENT Seconds FIGUE 8. otor esistance During Starting The final step in establishing e slip-dependent ermal model is incorporating e slip-dependent rotor resistance into e heat source of e ermal model shown in FIGUE. As mentioned before, e standard starting ermal element assumes a constant rotor resistance of pu across e entire speed range from standstill (S = ) to rated speed at rated shaft output (S = FLS). That value is M. Let us express e slip-dependent resistance value, r (S), in terms of its maximum value, M, and substitute it into e heat source equation: (S) W = I r = I (pu W) () r M Breaking () down into positive- and negative-sequence components accommodates motor heating due to balanced current (positive sequence) and any current unbalance (negative sequence) at might be present. (S) (S) W = I + I (pu W) () r TOTAL M eplacing e heat source of FIGUE wi () gives rise to e slip-dependent ermal model shown in FIGUE 9 []. r M I LA T STALL ( ) ( ) S S I + I M M FIGUE 9. Slip-Dependent Starting Element 8

9 The response curve for is modified starting element is shown in FIGUE otor Temperature U Motor Current Slip Dependent = ( M N )S + N Motor Torque Seconds FIGUE. Slip-Dependent Starting Element esponse Curve Comparison of e standard starting element response curve to e slip-dependent starting element response curve is shown in FIGUE. It clearly shows at because of e decreasing rotor resistance as a motor accelerates, rotor temperature is not a linear relationship, resulting in e ability to facilitate high-inertia starts wiout premature motor trips. TEMPEATUE Temperature (U/UL), otor OTO x. X OTO UNNING ELEMENT CUENT Current Current I t I elay t MOTO Motor Torque TOQUE otor Temperature SLIP DEPENDENT MOTO Motor Current CUENT SECONDS Seconds FIGUE. Comparison of Starting Element esponse Curves When motor current drops below.5 FLA, e rotor model switches from e rotor starting element to e rotor running element. At is point, e rotor starts its cooling process. The element resorts to e ermal C circuit shown in FIGUE. The parameters of e circuit are based on e rotor locked-rotor current and safe stall time and cannot be modified by e user. They are: trip = LA HOT U. I T C = 3. = LA HOT. I T 9

10 The circuit is illustrated in FIGUE.. I LA T HOT I r ( I + r I r). I LA T HOT The following facts can be observed at is time: FIGUE. otor unning Element When e rotor temperature stabilizes, e rotor ermal capacity is.67 I pu. The rotor cooling (and heating) ermal time constant is LA.6 I T s. HOT STATO POTECTION Equation () and FIGUE apply to e stator ermal model for bo starting and running motor states. To see e response of e model to current flow, let us solve () by rearranging e terms: du I r = C + U ( C) (3) dt The above equation is furer simplified by converting it to a pu quantity. The base quantities are: Full-load current = I FLA Temperature at rated current = FLA I r Convert (3) to a pu quantity: I r FLA I r du = I = C + U (pu C) (4) dt As in any C circuit, e product of C and represents e motor ermal time constant τ: du I = τ + U (pu C) (5) dt It is important to note at e quantity I represents pu temperature. In oer words, pu temperature is proportional to e square of e pu current.

11 Equation (5) is a first order linear differential equation whose solution is: where: U(t) = pu temperature as a function of time I = pu initial current I = pu final current τ = motor ermal running time constant t τ t τ U(t) = I e + I ( e ) (pu C) (6) Anoer useful presentation of (6) to motor relay engineers is e time in which e ermal model will reach temperature. ewriting (6) yields: I I t =τ ln I U(t) (s) (7) In plain language, (7) states at e time it takes to reach temperature is a function of e initial motor current, e final motor current, and e ermal running time constant. Two important reminders are: The base for is pu system is motor full-load current, FLA. A valid range for pu temperature, U(t), is anywhere between initial pu temperature, temperature, I. I, and final pu Let us furer simplify (7) to make it more suitable for motor protection applications. Manufacturers state e machine s service factor, SF, on every motor nameplate. Even ough e exact interpretation of e SF varies, one ing is certain any motor current greater an SF FLA is considered a running overload condition. Translate is into a maximum pu temperature at e motor is designed for and can sustain at any time: Because I FLA = pu, e above expression is furer simplified to: FLA U(t) = (SF I ) (pu C) (8) U(t) = SF (pu C) (9) Substituting (9) into (7) results in e final equation of e first order ermal model: I I t =τ ln I SF (s) ()

12 FIGUE 3 illustrates e stator model. I ( I + I) FIGUE 3. Stator Model A closer examination of () reveals at in order for time to be a rational number, e overload current, I, has to be greater an SF I FLA. The question en is: what happens in a case where I is less an SF I FLA? This situation does not constitute an overload condition but raer reflects e element s response to a load change. Let us revisit (7). Because e denominator has to be greater an zero to maintain a rational number, postulate (using e ree time constants rule, which states at it takes ree time constants for a quantity to exponentially decay to less an 5 percent of its original) at once e pu temperature, U(t), reaches wiin 5 percent (.5 pu) of e final pu temperature, I (increasing or decreasing), e equation is satisfied. I U(t) =.5 (pu C) () Substituting () into (7) and again accounting for increasing or decreasing loads, t is e time it will take e motor temperature to change from I to I : I t =τ ln =τ ln I I.5 I ( ) (s) () MOTO STOPPED STATE When a motor is de-energized, it does not require protection per se; however, it does need to be locked out and not allowed to re-energize until it cools down sufficiently to offer furer service. When current ceases to flow in e ermal circuit shown in FIGUE, e circuit reconfigures, as illustrated in FIGUE 4. FIGUE 4. Motor Stopped State The lockout state has e logic value of one only when U > U ESET. Oerwise, it is zero.

13 The lockout time can be calculated by substituting e following values into (7): Which leads us to lockout time, T LOCKOUT : I = I = %TC U(t) = %TC COOLTIME τ= 3 ESET T LOCKOUT COOLTIME %TC = ln 3 %TCESET (s) (3) This equation applies to e rotor and stator models. THEMAL MODEL ESPONSE CUVES The above presentation of e first order ermal model provides e maematical derivations to substantiate equations at constitute e dual first order ermal model. Just as important and probably more practical is e graphical representation of e dual first order ermal model. This set of curves and e motor manufacturer s ermal limit curves can be plotted togeer on a single graph to ensure at e model s settings do indeed protect e motor to e motor manufacturer s design specifications. FIGUE 5 is a typical set of curves describing e response of e dual first order ermal model. The slipdependent element of e rotor model is not shown because it is a dynamic algorim fed by e actual measured input impedance of e motor (used to calculate rotor slip and resistance). FIGUE 5. First Order Model esponse Curves 3

14 CONCLUSION Using e dual first order ermal model offers an accurate, ermodynamically based meod of tracking pu temperature of an ac motor. Starting or running, e dual first order ermal model provides a superior replica of motor pu temperature generated by motor current flow, ensuring at motor manufacturer s specifications are not exceeded, us preserving e integrity and design life of e machine. EFEENCES [] S. Zocholl, Optimizing Motor Thermal Models, proceedings of e 53rd Annual Petroleum and Chemical Industry Conference, Philadelphia, PA, September 6. [] S. Zocholl, AC Motor Protection, Schweitzer Engineering Laboratories, Inc., 3. VITAE Ed Lebenhaft received his BS in Electrical Engineering from e University of Toronto in 97. He spent 8 years wi Ontario Hydro, operating, en constructing, and finally designing nuclear power plants. In e following 4 years, Ed was a regional manager wi Multilin Inc. (later bought out by GE). After a brief retirement, Ed joined Schweitzer Engineering Laboratories, Inc. as a field application engineer dealing primarily wi motor protection. In September 8, Ed joined Calpine Corporation as a relay technical advisor. Ed is a registered Professional Engineer in Sou Carolina. Mark Zeller received his BS in Electrical Engineering from e University of Idaho in 985. He has broad experience in industrial power system maintenance, operations, and protection. Upon graduating, he worked over 5 years in e pulp and paper industry, working in engineering and maintenance wi responsibility for power system protection and engineering. Prior to joining Schweitzer Engineering Laboratories, Inc. in 3, he was employed by Fluor to provide engineering and consulting services. He has been a member of IEEE since Doble Engineering Company evolutionary Machines Seminar All rights reserved. 86 TP6338 4