21, rue d'artois, F-75008 Paris http://www.cigre.org A1-203 Session 2004 CIGRÉ DETERMINATION OF THE ACTUAL PQ DIAGRAM OF THE HYDROGENERATORS, BEING IN SERVICE, IN ORDER TO ESTABLISH THEIR MAXIMUM OPERATING DOMAINS AND THEIR CAPACITY TO PROVIDE SYSTEM SERVICES DAN ZLATANOVICI *, POMPILIU BUDULAN, RODICA ZLATANOVICI ICEMENERG (Romania) The theoretical PQ diagram represents the diagram of the reactive power versus the active power of a hydrogenerator, deduced from the phasorial diagram of the synchronous machine with salient poles. The actual PQ diagram is in fact a thermal diagram, in which the main theoretical curves represent the isotherms of the maximum admissible temperatures of the different parts of the electrical generator. Determination of the actual PQ diagram of the hydrogenerators being in service is performed in steady state operation, by measuring the maximum overheating appearing in the stator and rotor windings, in the stator core and in the frontal teeth sheets of the stator core. On the actual diagram, the secondary band is delimitated, where the produced or absorbed reactive power is paid, because the operation in this region is done with higher strains and costs. Measurements were performed on 25 hydrogenerators, with powers between 27 170 MW. Keywords: Hydrogenerator - PQ Diagram - Reactive Power - System service 1.INTRODUCTION The PQ diagram of synchronous generators is a synthetic diagram, delimiting the admissible operating domain, due to the heating of active parts and the static stability of the machine. The diagram is built in P active power and Q reactive power coordinates and it is valid for certain (usually rated) values of the generator terminal voltage, frequency and cooling agent parameters. Changing one of the parameters leads to changes in the diagram, by increasing or reducing the admissible operating domain. The diagram is very important for generators in operation because it shows the limit operating regimes and, on the other hand, it allows the immediate evaluation of the operating point with respect to these limits. It was found out during operation experience that a theoretical diagram (deduced from the phasorial diagram) and an actual PQ diagram (where the curves represent isotherms of the maximum admissible temperatures of different active parts) may be considered. The actual diagram has to be experimentally determined. Normally the two diagrams are identical. However, experience has demonstrated that for some hydrogenerators being in service for a long time, the two diagrams are not identical anymore, the actual one being more restrictive. This problem became important when the system service of voltage control, performed by the electric energy producers started to be a paid service rather than free. ICEMENERG, Bd.Energeticienilor 8, Bucharest, sector 3, Romania ; E-mail : danz@icemenerg.ro
On the actual diagram the secondary band is set off: there the produced or absorbed reactive energy has to be paid, because the operation in this secondary band is done with higher strains and hence higher costs. Most of the hydrogenerators in service in Romania have already operation lives of about 15 25 years or more and the actual operation limits are diminished; thus it was necessary to experimentally determine the actual PQ diagram. Measurements were performed on 25 hydrogenerators, 27 170 MW. 2. CONSIDERATIONS REGARDING THE PQ DIAGRAM 2.1. Theoretical PQ diagram The PQ diagram for hydrogenerators is derived from the phasorial diagram of the synchronous generator with salient poles, where the ohmic voltage drop is neglected [1,5]. Fig.1. Phasorial diagram for synchronous, salient poles generators Fig.2. Characteristic triangle of the PQ diagram Starting from the equations of the phasorial diagram in Fig. 1, the basic equations of the PQ diagram for hydrogenerators can be obtained: x q Id = E q U cos θ E d = U cos θ + x did (1) P = U I cos ϕ = U I a Q = U Isin ϕ = U Ir, (2) 2 U E d U 1 1 P = sin θ + sin 2θ (3) x 2 d x q x d 2 U E d 2 1 1 2 U Q = cos θ + U cos θ (4) x d x q x d x d where P,Q are the active and reactive power, respectively U - phase voltage of the generator I d - longitudinal component (along d axis) of the stator current x d, x q - longitudinal and transversal synchronous reactance E d, E q - longitudinal and transversal electromotive force θ - internal angle between the electromotive force and the terminal voltage. The ABC triangle from Fig. 1 converts into the characteristic triangle of the PQ diagram (fig. 2) by multiplying its sides by U / x d. 2
The PQ diagram is built as follows (Fig. 3): - point A is considered the origin of the coordinate axes P, Q; - with the radius AB = S n the BG circle arc is built; it represents the limit of the rated stator current on the current scale; the AB radius represents the rated stator current; - the semicircle with the diameter CO = U 2 (1/x q 1/x d ) is built at U 2 /x d distance from point A; - straight line CB is built; on the currents scale, the BC segment represents the rated field current and it is drawn through points from the condition: DB = D B = = OH; - the angle between the segment CB and the reactive power axis represents the internal angle θ between the electromotive force and the terminal voltage; - the EF curve represents the thermal limit of the frontal teeth sheets in capacitive regime; some manufacturers consider the capacitive operating limit as being a straight line traced depending upon the internal angle from point C up to the intersection with the active power limit; others consider the capacitive operating limit as being the static stability limit, with a 5-10% margin, starting from point C too, up to the intersection with the active power limit (CF curve); - the angle between the segment AB and the active power axis represents the phase difference ϕ between the current and voltage; - the zone in the right side of the active power axis represents the operating domain in inductive regime with reactive power production; point B is the rated operating point; the zone in the left side of the active power axis represents the operating domain in underexcited (capacitive) regime with reactive power absorption. Fig. 3. Theoretical PQ diagram of a hydrogenerator Fig.4. Actual PQ diagram of a hydrogenerator As a conclusion, the main limits are: rated field current limit, rated stator current limit, rated active power limit, turbine-imposed limit, thermal limit of the frontal zone for the capacitive regime and the natural static stability limit with a margin of about 5-10%. 1.2. Actual PQ diagram In fact, the actual PQ diagram is a thermal diagram, in which the main theoretical curves are isotherms of the maximum admissible temperatures of different active parts of the electrical generator (Fig. 4). Therefore, the stator current limit represents the stator winding isotherm (2), the field current limit represents the rotor winding isotherm (3), the capacitive regime limit represents the frontal teeth isotherm (5) and the turbine power limit represents the rated active power isotherm (1). On the actual diagram the following limits are represented, too: - minimum active power limit, due to some restrictions in the hydraulic turbine operation (4); - minimum field current limit, due to some restriction imposed by the excitation system, automated voltage controller and generator protections (7); - natural static stability limit with a 10% margin (6), which sometimes is more restrictive than the thermal limit of the frontal zone. Ideally, for new generators or for generators that had an easier operating regime (operation at the base of the system's load line) the two diagrams are practically identical. 3
For generators with a large number of service hours and with heavy operating regime (operation at the top of the system's load line or in a continuous frequency - power control regime), the two diagrams are no longer identical. The actual PQ diagram becomes more restrictive due to aging in the sensible elements of the generator: stator winding, rotor winding, stator core, worsening of the ventilation and cooling conditions, etc. and due to some phenomena such as the increase of vibrations level, cavitation etc. Until the deficiencies are repaired or until a complete rehabilitation is performed, these generators have to operate with restrictions according to the actual PQ diagram. The thermal limits can be determined by measuring the maximum heating in the stator and rotor windings, the stator core and the frontal teeth sheets in steady state thermal regimes. The actual PQ diagram is obtained as the intersection of the theoretical diagram (drawn for the rated parameters: voltage, frequency, cold air temperature) with the thermal limits of the experimentally determined thermal diagram. The curve delimiting the mimimum area is kept as the final PQ diagram: therefore, both the conditions of nonexceeding the maximum stator and rotor currents values and those of nonexceeding the maximum admissible heating of the active elements of the generator are satisfied. 3. ACTUAL PQ DIAGRAM DETERMINATION The determination of the actual PQ diagram consists in determining the locus of all operating points where the maximum heating in the active parts of the generator (stator copper, stator magnetic core, frontal teeth, rotor winding) does not exceed maximum admissible limits. The insulation system of the hydrogenerators made in Romania allows for 120 o C maximum temperature of both stator bars T ), and magnetic core steel sheets insulation ( T Fe max ). For the polar coils of the field winding the maximum allowed temperature ( T f max ) is 130 o C. Consequently, the maximum admissible overheating of the generator s active parts over the cold air inlet temperature ( T ca ) is: ( Cu max θ( Cu,Fe,f ) max = T( Cu,Fe,f ) max Tca (5) The method for establishing the actual operating limits of a hydrogenerator in steady-state inductive regime consists in determining the maximum heating in the copper bars of the stator winding, the stator magnetic core and the field winding. The measurement of the temperatures of these elements is performed as follows: for the stator winding bars and the stator core - using Pt 100 thermoresistances, mounted (at generators manufacturing) between the bars placed in the same slot and between the bottom stator bar and the bottom of the slot, respectively; because there are no thermal transducers on this winding, the temperature of the field winding has to be measured indirectly, using the resistance variation method; thermometers are installed on the air coolers for the inlet and outlet to measure air temperatures; the existent thermoresistances are also used. The actual maximum admissible limit for the steady-state inductive regime is determined in PQ coordinates, based on these measurements. The method for establishing the actual operating limits of a generator in the steady-state capacitive (underexcited) regime requires measuring the maximum overheating in the frontal pack teeth. The supplementary heating of the frontal packs of the stator core in a capacitive regime appears due to the increase in the leakage magnetic flux and especially of its axial component, traversing only these packs. In the capacitive regime the armature reaction is magnetizing and it adds to the main inductive flux (in the inductive regime the armature reaction is demagnetizing, so the two fluxes are subtracted). The supplementary losses, mainly due to the increase of the axial component of the leakage flux cause additional heating in the frontal packs. The supplementary heating in this regime affects both the insulation of the frontal teeth sheets, and stator winding bar, with which the frontal teeth are in full contact. If the maximum admissible thermal limits are exceeded, the consequences are: failure of the insulation between sheets up to local melted points and premature aging of stator bars insulation up to failure. In order to measure the heating of the frontal pack of sheets in capacitive regimes, an experimentaltheoretical hybrid method was used [2,3,5], consisting mainly from the following steps: 4
- temperature and magnetic field sensors are mounted on the frontal face of the first frontal stator pack and in the first radial ventilation channel (Fig. 5) for about 10 stator teeth; - based on the overheating and flux densities measured on the boundary of the frontal pack of sheets, the losses and the overheating inside it are determined in the nodes of a discrete network by using a computer program called TEMP [3,5]; the hottest point is localized this way for every capacitive operating regime. Also, the variations of the overheating in that point are determined as a function of the reactive power Q at different active power P levels. - The operating thermal limits in the capacitive regime are determined using the θ = f (P, Q) curves, for the maximum admissible temperature of the sheets and stator winding insulation. The above described method is precise and applicable; it was verified by studies on real laboratory models and on a real generator in cooperation with the manufacturer [4,6] a b Fig.5. Mounting of the measuring transducers for temperature and magnetic flux density; a - mounting outline for the devices with transducers; b devices mounting in the frontal zone; 1 rotor pole; 2 pressing piece; 3 frontal pack of sheets; 4 the second frontal pack of sheets; 5 frontal device ; 6 ventilation channel device. 4. DELIMITING OF THE SECONDARY BANDS ON THE ACTUAL PQ DIAGRAM System services are defined as services usually provided by the producers, at System Operator s demand, in order to maintain both the safety level of the National Energetic System (NES) and the quality of the transported energy, within specified standard parameters [8,9]. System services are paid with prices set by Romanian Electricity Regulatory Authority. Until recently, the system services were not paid in Romania. In the context of a developing energy market in Romania and of interconnecting the Romanian system with the EU system (UCTE), it was suggested that system services be compensated through payment since they can't be provided without expense by the energy producers. One system service, with special implications concerning the generators capacity to provide it, is voltage control. This control is performed by producing or absorbing electric reactive energy by the generators connected to NES, according to the reactive versus active power (PQ) operating diagram of the group. The capability for providing this system service is mandatory and a condition for each group to be connected to the electric network. In this context, Romanian Electricity Regulatory Authority decided to split the PQ diagram of the generators into two types of bands: - the primary band, defined as the region of a synchronous generator PQ diagram in which the produced or absorbed reactive energy is not paid; - the secondary bands, defined as the regions in the PQ diagram where producing or absorbing reactive energy incurs higher costs and high wear of the generator. In these regions the reactive energy produced or absorbed on System Operator s demand is paid. Romanian Electricity Regulatory Authority did not establish criteria for delimiting these bands, leaving the problem to the competence of the technicians and managers of the system services producers and of the commercial and system operators. 5
In Europe the problem is not unitary settled yet and each country applies its own system [10]. In some countries the inductive and capacitive power factors are imposed; these power factors delimit the domain on the PQ diagram, inside which the produced / absorbed reactive power is not paid; outside this domain and up to the limits of the PQ diagram the produced / absorbed reactive energy is paid. The value of the inductive power factor varies between 0.85 0.928 and the capacitive power factor varies between 0.95 0.989. In other countries the produced / absorbed reactive power is not paid, considering that the investment for metering and registering is not justified with respect to the offered price. Also, there are countries where the produced / absorbed reactive energy is paid only for networks below some voltage levels, based on special contracts between the energy producer and the System Operator. Several criteria were proposed in Romania to establish the boundary between the primary and secondary bands of voltage control, inside the maximum limits of the PQ diagram. One of the criteria consists in the delimitation of the secondary bands by the isotherm curves of the rotor winding and stator frontal zone; beyond these isotherms, for a certain active power, by increasing the reactive power, the temperature exceeds 90 o C for one or more of the active elements of the generators (stator copper and magnetic core, field winding). Taking into account the age and the upto-date state of the hydrogenerators, it was considered that operation above 90 o C leads to a more accelerated aging of the insulation and, consequently, to a shortening of their lifetime; thus, the necessity to compensate the wear implied by the operation at higher temperatures (but inside the limits of the insulation class) through payment of the reactive energy was justified. Another proposed criterion was to translate maximum limits for the rotor and frontal zone of the actual PQ diagram up to 70% from the reactive power (curves 1 in Fig. 6). These limits correspond to some isotherms having temperatures below the maximum admissible limits for the rotor winding and the frontal zone. This criterion is agreed temporarily by the System Operator, being easier applicable once the actual PQ diagrams are already determined. HIDROELECTRICA Company, which currently owns all the hydrogenerators in Romania, agreed on another criterion. The straight lines of 0.975 inductive and capacitive power factors are drawn; for the inductive domain, from the intersection point with the maximum active power limit, a straight line is drawn symmetric with the line cos ϕ = 0.975 with respect to the ordinate of the intersection point, up to the intersection with the limit of the minimum active power; from this point, a vertical line is drawn up to P=0. For the capacitive domain, from the intersection point of the line of cos ϕ = 0.975 with the maximum active power limit, a vertical line is drawn up to P=0. The domains in which the produced / absorbed reactive energy is paid are those between these lines and the maximum limits of the PQ diagrams, and in the domain between the two lines (lines 2 in Fig. 6) the reactive power is not paid Fig.6.Criteria for delimiting the secondary bands: 1- the 70% criterion; 2- the cosϕ = 0.975 criterion. Fig.7. Actual PQ diagram of an A-class hydrgenerator. The negotiations between the company producing electric energy and the System Operator are not finished yet. However, the System Operator preliminary qualified some of the hydrogenerators for the 6
system service of voltage control on the base of the 70% criterion applied to the theoretical diagram. Also, the activity of installing adequate metering systems for the produced / absorbed reactive energy is only at the beginning. 5. SYNTHESIS OF EXPERIMENTAL RESULTS The actual PQ diagram was experimentally determined for a number of 25 hydrogenerators with powers between 27 170 MW (6 x 27 MW, 7 x 50 MW, 9 x 80 MW, 3 x 170 MW). In order to delimit the secondary bands, the cos ϕ = 0.975 criterion was applied. 3 classes of hydrohenerators turned out: Class A: the actual diagram is identically superimposed with the theoretical diagram (considering the limits of the minimum field current and the minimum active power) and the secondary bands of voltage control have the maximum area. 12 hydrogenerators belong to this class (Fig. 7). Class B: the actual diagram is more restrictive than the theoretical diagram, the operating domain having an area diminished by about 10-20% when compared to the theoretical domain. The areas of the secondary bands are correspondingly diminished. 5 hydrogenerators belong to class B. The reductions are due to some temperatures of the rotor winding greater than the admissible limit, generally appearing for powers greater than 70% from the rated power. The probable cause of this phenomenon is represented by the worsening of the cooling conditions of the rotor winding, due to the sagging of the polar coils towards the exterior part of the poles and therefore clogging of ventilation channels (fig. 8). Class C: the actual diagram is very restrictive whe comapared to the theoretical diagram, the operation domain being diminished by about 20 60%. For this reason, the areas of the secondary bands of voltage control have correspondingly reduced surfaces. 8 hydrogenerators were assigned to this category. The causes of these narrowings are different. Two hydrogenerators cannot operate with power greater than 54% from the rated power due to increased vibration level in the rotor, caused by an improper constructive solution for poles mounting. Other 5 hydrogenerators have powerful heating in the frontal zone of the stator. The expertises performed shown the existence of great losses in the frontal packs of sheets of the stator teeth, a poor ventilation of these frontal packs of sheets, an increased air temperature in the airgap and increased temperatures of the outlet cool air. All of these elements lead to limitations in the inductive domain, by exceeding the admissible temperatures either of the stator winding or of the stator core (Fig. 9). Another hydrogenerator, due to its geographic position in the network at the end of a 110 kw line, has its static stability limit so restrictive that it cannot operate in the capacitive domain. Supplementary, due to an inadequate constructive solution, the ventilation in the frontal zone is very weak. All of these hydrogenerators are to be included in a rehabilitation and modernization program, in order to eliminate their deficiencies and enlarge their operating domain. Fig. 8.PQ diagram of a B-class hydrogenerator (theoretical diagram with thin line) Fig. 9. PQ diagram of a C-class hydrogenerator (theoretical diagram with thin line) 7
In the figures 7, 8 an 9 - Q1 represents the secondary band for produceing reactive power and Q2 is the secondary band for absorbing reactive power. 6. CONCLUSIONS The actual PQ diagrams difer from the theoretical PQ diagram for an important number of hydrogenerators currently in service. For this reason, the actual PQ diagram has to be determined for every hydrogenerator. The determination of the actual PQ diagram allowed an evaluation of the present condition of every hydrogenerator and a precise delimitation of their actual operating limits. Some deficiencies were revealed and actions for their elimination were scheduled. Some deficiencies are due to design flaws, others are due to improper maintenance. REFERENCES [1] Walker J.H., Operating characteristics of salient-pole machines, (IEEE vol.100, part II, 1952) [2] D. Cretu, D.Zlatanovici and others, The operation of large low-speed hydroelectric generators under abnormal and special conditions, (Proceedings of the CIGRE, group 11, Paris 1972, Rapp.11-07) [3] Dan Zlatanovici, Direct Experimental Method for Determining Thermal and Magnetic Stresses at the Frontal Stator Tooth of Generators in Operation,(Rev. Energetica Romania, vol.31, nr. 9, 1983, p.412-417). [4] D.Zlatanovici, The Study of the Magnetic and Thermal Field inside the Frontal Stator Teeth of Synchronous Generators, on a Physical Electromagnetic Model, ( Rev. Energetica Romania, 6, 1983, p.281-284) [5] Dan Zlatanovici, "Contributions to the study of the electromagnetic phenomena in the frontal zones of the high power electrical machines" (Ph.D. dissertation, Dept. Electrotechnical Eng., Univ. Politehnica Bucharest,1987) [6] Dan Zlatanovici, Magnetic and thermal stresses of the frontal stator teeth of 330 MW turbogenerators, (Rev. Energetica Romania, 4-5, 1989, p.190-195). [7] Dan.Zlatanovici and other, Technologies for "on line" diagnosis, data logging and prediction at turbogenerators", (Proceedings of the CIGRE, group 11, Paris, 1996, Rapp.11-204) [8] CN Transelectrica SA, "Technical code of the electrical transport network", Cod 51.1.112.0.01.07, 2000, (Available: www.transelectrica.ro) [9] Romanian Electricity Regulatory Authority -ANRE, "Methodology for establishing the system services tariffs", Code 35.1.432.1.01,1999, (Available: http://www.anre.ro) [10] R. Hirvonen, R. Beune, L. Mogridge, R. Martinez, K. Rouden, O. Vatshelle, Is there market for reactive power services Possibilities and problems, (Proceedings of the CIGRE, group 39, Paris, 2000, Rapp.39-213) 8