1 2006 IEEE PES Transmission and Distribution Conference and Exposition Latin America, Venezuela Synthetic and Systemic Model for Power Quality Evaluation J. A. Lopera, A. E. Díez, J. A. Bohórquez, G. J. López, I. C. Díez, and S. Mesa A. Signal nullity subject to effect’s nullity Each indicator’s value must be zero when PQ phenomena measured (by the indicator) is not present in the system. B. Increment due to PQ phenomena’s severity Each indicator’s value must increment phenomena’s severity increment. when PQ C. Defined compatibility limit for the indicator Each indicator must have a defined compatibility limit. When this limit is exceeded, energy supplied is inadequate for use in sensitive equipment. This is in order to ensure for electromagnetic compatibility. III. Index Terms--Flicker, Harmonics, Power Quality, Power Systems. I. INTRODUCTION P ower Quality (PQ) phenomena have been evaluated in an independent way using indicators like PST (Defined in Std. IEC 61000-4-15) and THDV (Defined in Std. IEEE 519). PST indicator represents voltage fluctuation’s severity, using lamp-eye-brain system as reference (PST = 1 pu represents a flicker level that’s annoying to 50% of the population). THDV indicator evaluates the percentage of energy supplied at frequencies different from system’s nominal frequency. This means that PQ indicators, such as the ones described before, possesses an independent physical meaning. Simultaneous presence of PQ phenomena in power systems calls for an indicator that’s able to integrate simultaneous effects using information from usually measured PQ indicators, such as the ones described above. However, to assure simultaneous evaluation’s adequacy, indicators must comply with some physical and mathematic properties. II. INDEPENDENT PROPERTIES Before integrating indicator’s definition the compliance with some properties is required. The first three properties are evaluated in an independent way. ORTHOGONAL SPACE FOR INDICATOR’S INTEGRATION Using linear algebra’s concepts, formal establishment of an orthogonal space that ensembles PQ indicators is achieved. Orthogonal space concept requires, among other things, linear independency between indicators, which, in this case, means that when a specific PQ phenomenon’s severity increments, only the value of the associated indicator must increment. Defining inCEM, as a vectorial space in n called Electromagnetic Incompatibility, with internal product and norm (inCEM,<>,|| ||). If X and Y are a couple of vectors that belong to inCEM, X and Y are orthogonal if their intern product is zero (<X, Y> = 0). This property extends to any couple of unitary vectors Ci y Cj. In this case, every unitary vector points out toward a specific PQ phenomena direction. Normalization is achieved by dividing each indicator by its compatibility limit, as defined in (1): PQ (1) PQinC UmbPQ Where, PQ: PQ indicator (PST, THDV, …). PQinC: Normalized value of PQ indicator. UmbPQ: Compatibility Limit for PQ indicator. This procedure also guaranties dimensional unification in compatibility levels, and allows the definition of the orthogonal space called Total Degradation (DT). IV. VERIFICATION OF THDV AND PST PROPERTIES A. Signal nullity subject to effect’s nullity PST and THDV indicators yield zero, when they’re 1-4244-0288-3/06/$20.00 ©2006 IEEE 2 B. Increment due to PQ phenomena’s severity The following figures show how PST and THDV comply with this property. Instantaneous Flicker [pu] 4000 3500 0.30pu (PST=5.0617) 0.20pu (PST=3.5730) 3000 0.15pu (PST=2.7541) 0.8 THD 0% 0.6 THD 10% 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 2500 -1 0 2000 1500 2 4 6 8 10 12 Time [miliseconds] 14 16 18 Fig. 4. Increment in THDV value due to an increment in distortion. 1000 500 0 49.5 C. Defined limit for the indicator 50.0 50.5 51.0 Time [seconds] 51.5 52.0 Fig. 1. Increment in PST value due to an increment in voltage change, 'V. 2000 100ms (PST=3.5730) 1800 Instantaneous Flicker [pu] 1 Instantaneous Voltage [pu] measured over the standard waveform (Senoidal wave at system’s nominal frequency and with an amplitude of nominal voltage times 2 ). 1600 20ms (PST=1.9937) TABLE I 10ms (PST=1.0691) THDV LIMITS 1400 Nominal Voltage UmbTHDV (%) V < 69 kV 5.0 69 kV V < 161 kV 2.5 V 161 kV 1.5 Those values have been defined taking in account the sensitivity of end user’s equipment. 1200 1000 800 600 400 200 0 49.5 A limit for PST is found in Std. IEC 61000-3-7. This standard recommends PST = 1pu (UmbPST) as a limit in low and medium voltage systems. A limit for THDV, for each nominal voltage, is found in Std. IEEE-519 [1992]. This standard recommends the following limits, in function of nominal voltage. 50.0 50.5 51.0 Time [seconds] 51.5 52.0 Fig. 2. Increment in PST value due to an increment in duration of voltage fluctuations. 3500 D. Orthogonallity The requirements found Std. IEEE-519 for a THDV instrument response (especially dynamic response and bandwidth) and the requirements found Std. IEC 61000-4-15 for a PST instrument (especially the weighting filters defined in block 3) , guaranties orthogonallity between PST and THDV. Instantaneous Flicker [pu] 2 (PST=5.7449) 3000 V. INTEGRATION OF VARIABILITY AN NON LINEALITY EFECTS 1 (PST=3.5730) 2500 2000 1500 1000 500 0 49.5 50.0 50.5 51.0 Time [seconds] 51.5 52.0 Fig. 3. Increment in PST value due to an increment in the number of voltage fluctuations. When the independent properties and orthogonallity of some PQ indicators (PST and THDV in this case) is guarantied a Total Degradation space can be defined. In this case (1) yields: PST THDV inC (2) PST , THDVinC UmbPST UmbTHDV Equation (3) shows Total Distortion Vector (DTPQ) in its polar form: 2 2 § PST · § THDV · ¨¨ ¸¸ ¨ ¸ T (3) UmbP UmbTHDV © ¹ ST ¹ © Where Ԧ is the angle between PST’s component y and THDV’s component, as shown in Fig. 5. DTPQ 3 Fig. 6. DTPQp vector VII. CONCLUSIONS Fig. 5. DTPQ vector VI. DTPQ VECTOR’S MAGNITUDE Taking in account the properties defined for DTPQ’s components (and verified for PST y THDV in this case) is possible to demonstrate that DTPQ vector’s magnitude has a direct relation with the quantity of energy that even though it has been delivered, it can’t be adequately used, and on the contrary it affects end user equipment. This energy is called bad supplied energy. If DTPQ vector’s magnitude is greater than 1, there are PQ problems regarding voltage fluctuations and harmonic distortion. If angle Ԧ tends to 90 degrees, impact of harmonic distortion (due to non-lineal loads) is greater than impact of voltage fluctuations (due to fluctuating loads). This issue it’s needed in order to determinate the problem and to take corrective actions. In polyphase systems a third component (compliant with defined properties) which measures voltage unbalance can be added. This indicator, called Vumb, measures polyphase system’s unbalance in magnitude and angle by measuring the relative size of negative and positive sequence components. Vumb indicator is calculated as shown in (4): V (4) Vumb 100% V Where, V-: Negative sequence voltage at fundamental frequency. V+: Positive sequence voltage at fundamental frequency. A limit for Vumb is usually 2% (UmbVumb). In this case (1) yields: Vumb (5) VumbinC UmbVumb Fig. 6 shows DTPQ vector in polyphase systems – DTPQp: The model proposed in this paper allows synthetic (because it homologues and superpose various phenomena) and systemic (oriented to system’s performance) evaluation of PQ using voltage information processed using measuring devices currently available at the utilities, like flicker and harmonic meters. The orthogonallity property assures that DTPQ vector’s magnitude correctly reflects system’s incompatibility level. A general methodology for new indicator’s validation and inclusion was developed. Therefore, other components can be added in order to measure the integrated effect of more types of PQ phenomena, such as impulsive transients. Adequate measuring methodology, like the one described above, is the first step toward efficient assignation of PQ responsibilities. VIII. REFERENCES [1] [2] [3] J. A. Blandón, Procesamiento de medidas de resistividad. Medellín: IEB, 1989, 123p. M. Bollen, Understanding Power Quality Problems: Voltage Sags and interruptions. New York: IEEE Press, 2.000, 200 p. IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems, IEEE Standard 519-1992, Apr. 1992. IX. BIOGRAPHIES Jairo A. Lopera was born in Colombia in 1.965. He graduated form Electrical Engineering at Universidad Pontificia Bolivariana in 1.987. He graduated form T&D’s Specialization at Universidad Pontificia Bolivariana in 1.995. He obtained his MSc title in 2.005. From 1.987 to 1.988 he worked for P&R Ltd as Resident engineer. From 1.988 to 1.996 he worked for UPB as teacher. He has been dean since 1.996. He’s member of T&D Research Group at UPB. [email protected] Andrés. E. Díez was born in Colombia in 1.979. . He graduated form Electrical Engineering at Universidad Pontificia Bolivariana in 2.001. He graduated form T&D’s Specialization at Universidad Pontificia Bolivariana in 2.005. He obtained his MSc title in 2.005. He has been teacher at UPB and engineer at “Maquinas Industriales” since 2.001. He’s member of T&D Research Group at UPB. [email protected] José. A. Bohórquez was born in Colombia in 1.965. He graduated form Electrical Engineering at Universidad Pontificia Bolivariana in 1.989. He graduated form T&D’s Specialization at Universidad Pontificia Bolivariana in 1.996. He obtained his MSc title in 2.004. From 1.989 to 1.990 he worked for “Textiles Panamericanos Ltda” as Electrical department chief. In 1.990 he worked for Fabricato. Since 1.990 he’s teacher at UPB. Since 1.992 he’s teacher at EAFIT University too. He has been Electrical Engineering Lab’s chief since 1.999. He’s member of T&D Research Group at UPB. [email protected] 4 Gabriel J. López was born in Colombia in 1.980. He graduated form Electrical Engineering at Universidad Pontificia Bolivariana in 2.001. He graduated form T&D’s Specialization at Universidad Pontificia Bolivariana in 2.005. He’s member of T&D Research Group at UPB. [email protected] Iván C. Díez was born in Colombia in 1.982. He graduated form Electrical Engineering in Universidad Pontificia Bolivariana in 2.004. In 2.004 he was awarded by Colombia’s national government for his good results in the undergraduate quality exams – ECAES-. From 2004 to 2005, he advised “Comisión de Regulación de Energía y Gas” – CREG – in Reactive Power, transmission and LPG issues. Currently he’s studying T&D’s specialization at UPB and teaching at UPB. [email protected] Santiago Mesa was born in Colombia in 1.980. From 2.001 to 2.003, he worked as Matlab Monitor/Teacher at Universidad Pontificia Bolivariana. In the second semester of 2.003 he worked at Interconexión Eléctrica SA (ISA) as practice student. He graduated form Electrical Engineering in Universidad Pontificia Bolivariana in 2.003. In 2.004 he was awarded by Colombia’s national government for getting the first place in the undergraduate quality exams – ECAES-. From 2004 to 2005, he advised “Comisión de Regulación de Energía y Gas” – CREG – in PQ and power market issues. Nowadays he’s working at CIDET and he’s member of T&D Research Group at UPB. He’s currently studying T&D’s specialization at UPB. [email protected].
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