Harmonics proliferation in power distribution system due to the increasing use of nonlinear load has become one of a major power quality problem for both customer and supply side. The harmonic power losses can lead to both increased operational costs and to additional heating in power system components, which in turn might reduce their expected lifetime. A great amount of different component can be found and a large number of insulated cables are frequently used in typical electrical power system. In general the cost of power quality and in particular the aging costs due to harmonic losses in transformers will increase since harmonics will affect all power system equipment. The effects of harmonic on power system equipment are explained in great detail in many publications [3, 4, 6-10, 12-14, 16, 18, 20-24, 26, 27, 29-31, 43, 44, 45, 47]. Different investigation about the consequence of a poor quality supply in power system equipment have been reported, very little have been said about the financial aspects of this phenomenon [4, 10, 11, 15, 21, 44, 45].
Harmonic Effect on Transformers
Transformers are one of the component and usually the interface between the supply and most non-linear loads. The effects of harmonic on the performance of this component represent a matter of major importance [7]. Increased in harmonic distortion component of a transformer will result in additional heating losses, shorten insulation lifetime, higher temperature and insulation stress, reduce power factor, lower productivity and capacity and lack of performance of the system [20]. Transformer losses are generally classified into no-load loss and load-related loss. No-load losses are the losses due to the voltage excitation of the core. The load loss can be dividing into Pdc losses (I2Rdc) and stray losses [2]. The stray load losses are caused by electromagnetic fields in the windings, core, core clamps, magnetic shields, enclosure or tank walls, and other structural parts [10].
Both No load & Load losses are affected by the presence of harmonics in load currents. But the variation in load losses contributes more to excessive heat generation in distribution transformer. Increment in no load losses in a distribution transformer due to harmonics is less compared to the load loss but it has a significant contribution to the capitalization cost when operating in longer term.
Ref: Power System Harmonic Effects on Distribution Transformers and New
Design Considerations for K Factor Transformers
N.R Jayasinghe*, J.R Lucas#, K.B.I.M. Perera**
In general, harmonics losses occur from increased heat dissipation in the windings and skin effect both are a function of the square of the rms current, as well as from eddy currents and core losses [1]. This extra heat can have a significant impact in reducing the operating life of the transformer insulation. The increased of eddy current losses that produced by a non-sinusoidal load current can cause abnormal temperature rise and hence excessive winding losses. Therefore the influence of the current harmonics is more important, not only because of the assumed square of the harmonic order but also because of the relatively large harmonic currents present in the power system.
Antonia et al. [7] and Radmehr et al. [47] study the effect of harmonic on power transformer loss of life. The transformer loss of life estimated using frequency domain technique [7]. In [47] the loss of life of transformers in presence of harmonic has been calculated using real data and the transformer life compared with the per unit load in presence of harmonic, higher load lower the life of the transformer due to current harmonics generated by the electrical drive.
In the following some literature dealing with the harmonic effect on transformers was cited. Aleksandar [18] discussed on the measurement and evaluation of transformer losses under linear and non-linear loads. The measurement of a transformer's losses and calculation of its efficiency is very well understood and applied in the power and distribution transformer industry. Harmonic voltage increase losses in its magnetic core while harmonic currents increased losses in its winding and structure [18]. Three method of estimating harmonic load content are practiced, which are the crest factor and harmonic factor, %THD are the two most common methods of harmonic estimation but limited because harmonic frequencies are not considered, and K-Factor is the most complex, but the most meaningful [26]. Massey [26] recommend that electrical designer utilize the K-Factor calculation and proposed adaptation of the K-Factor when specifying dry-type power distribution transformers intend to supply non sinusoidal current drawing load. Jayasinghe et al [3] studied a new design technique for K-factor transformer. L.Ran [12] presented an analytical method to calculate the core losses in a distribution transformer supplying non-linear loads.
The distribution of flux in the core is derived using the magnetizing voltage obtained from a series of frequency domain harmonic equivalent circuits. The flux which contents harmonic is then used to calculate the eddy current and hysteresis losses and approximation were proposed for the B-H relationship, which the method is verified by experiments [12]. Cost of core losses and load losses will be developed with a specific set of three phase coils having cores made from several commonly used core materials [21]. Transformer are normally designed and built for utilizing at rated frequency and linear load current. Supplying non-linear loads by transformer lead to higher losses, reduction of the useful life of transformer, premature detective and early fatigue of insulation. To prevent these problems rated capacity of transformer supplying non-linear load must be reduced [24]. Manufacturer of distribution transformer have developed a rating system called K-Factor, a design that is capable of withstanding the effects of harmonic load currents [3].
Harmonic Effect on Cables
In the cable cases, current and voltage can cause additional losses in the conducting and in the insulating materials that cable life reduction will arises if they are neglected in the cable sizing [8, 9, 14, 22, 23]. The evaluation of the cable size in the nonsinusoidal operating condition has been analyzed in literature [13, 16, 29]. In [13, 16] the procedure presented are base on ampacity considerations without particular attention to the total cost that can be suffered in the entire cable life, only in [29] considerations on the effects of harmonic loss cost on cable size are given. The larger of harmonic, the higher are the conductor losses, so for the most economical cable section the larger conductor sizes are need.
Harmonic in distribution cable systems cause increased ohmic losses and increased operating temperatures [13]. The ampacity of the cable determined by the ohmic losses of cable system and the ability of its surrounding to remove the heat generated, where the ohmic losses are dependent upon the presence and magnitude of harmonic current [13]. A basic electrical and thermal concept was approached to quantify cable temperature and life expectancy [9]. Figure 4 shows result related to the cable temperature under different levels of applied voltage distortion. The voltage distortion is represented by the THVD% and it can be seen the range of variation goes from 0 - 12% which represents typical industrial values [9]. It can be concluded that the voltage distortions produce minor effect upon cable life expectancy. A different techniques use to evaluate the relationship between harmonic current distortion and cable life expectancy. It consists in applying currents generated from ideal current sources. The current distortion is define by the THDI% and the range of variation used varied from 0 - 25%, and also present the typical installation distortion [9]. In figure 5 it can be seen that the harmonic current cause a much greater effect upon cable useful life [9].
Figure 4: Life expectancy versus harmonic voltage distortion.
Figure 5: Life expectancy versus harmonic current distortion
The current distribution in cables is affected by the skin effect and the proximity effect due to neighboring cables of the circuit itself or from parallel links [27]. The flow of normal fundamental frequency current in a cable produces I2R losses and the current distortion introduces additional losses in the conductor. The effective resistance of the cable increased with frequency due to skin effect, where unequal flux linkage across the cross section of the cable causes the ac current to flow on the outer periphery on the conductor [10]. This will reduce the ability of the conductor to carry current by reducing the cross sectional diameter of the conductor and thereby reduce the ampere capacity rating of the conductor. The higher harmonic frequencies cause a greater degree of heating in conductors because the skin effect increases as frequency and amplitude increase. The proximity effect exists because the electromagnetic field of cables in proximity can interact with each other, causing the resistance of cables to increase [10]. Table II [10] shows the losses in cables when considering and neglecting the skin and proximity effect, where the different between the values is low, but the harmonic related losses are significant, especially in cables 3 and 4. The effect of non-sinusoidal voltage on intrinsic aging of cable and capacitor insulating material was also investigated [8]. The effect of supply voltage distortion on intrinsic aging of cable can be considerable and depend mostly on the voltage peak increase due to distortion.
Table II: Losses in cables
Harmonic Measurement.
The parameters need to consider in evaluating harmonic distortion problems, is the voltage and current waveforms [1]. This is because other parameters, such as real, reactive, and total power; energy; and even unbalance, can be calculated from these two quantities but Thunberg and Soder [28] inform that to be able to use harmonic measurement in such calculation it required to have an accurate measurement of not only the harmonic voltage and current magnitude at all buses in the system but also the phase angles.
The important purpose for conducting harmonic measurements are to verify the order and magnitude of harmonic currents at the substation and at remote locations where customer harmonic sources may be affecting neighboring installations, to determine the resultant waveform distortion expressed in the form of spectral analysis, to compare the preceding parameters with recommended limits or planning levels, to assess the possibility of network resonance that may increase harmonic distortion levels, particularly at or near capacitor banks, to gather the necessary information to provide guidance to customers in controlling harmonic levels within acceptable limits, to verify efficacy of implemented harmonic filters or other corrective schemes and to determine tendencies in the voltage and current distortion levels in daily, weekly, monthly or yearly [1].
The main location where is the most measurements are conducted is the customer utility interface [18, 28, 47]. This is so because compliance with IEEE and IEC harmonic limits must be verified at this location. In customer owned transformer locations, the point of common coupling (PCC) is the point where the utility will meter the customer, generally the high-voltage side of the transformer. If the utility meters the low voltage side, then this becomes the PCC [1]. A harmonic power loss is one of harmonic issue that has many problems with harmonic measurement and has become of more interest [4, 22]. A few minutes recording may be sufficient and averaging over a few seconds should meet the requirements under steady-state operation and where no loading variations occur. In most of situations measurements over a few days may be needed to assure that load variation patterns and their effects on harmonic distortion are considered when the changing nature of loads occurs. For the long-term effects relate to thermal effects on different kinds of equipment such as transformers, motors, capacitor banks, and cables from harmonic levels sustained for at least 10 min and a very short-term effects relate to disturbing effects on vulnerable electronic equipment by events lasting less than 3s, not including transients [1].
Harmonic measurements are expensive in term of time and equipment and it possible to perform the measurement at all buses in the system. The accuracy of the measurement depends on the type and accuracy of the measurement instrument and the voltage and current transformer used. The measurement has to organize carefully and combined with some of the general knowledge about the system studied, the mathematical tool might be used to estimate some of the missing information and need to perform the calculation [28].
Economic Evaluation of Harmonic.
The quality of power can have a direct economic impact on utilities, customers and specific equipment. The economic effects of harmonics are shorter equipment lifetime, reduced energy efficiency and a susceptibility to nuisance tripping. Shorter equipment lifetime can be very expensive. Equipment such as transformers is usually expected to last for 30 or 40 years and having to replace it in 7 to 10 years can have serious financial consequences [43]. The cost of avoidance is relatively small, requiring only good installation practice and proper equipment selection. Installing cables that are one to two sizes greater than the calculated minimum reduces losses and operating costs at very little increase in initial cost.
Many papers can be found dealing with the cost of energy losses and premature aging [4, 22, 23, 44, 45] but practically no contribution refers to the misoperation cost. The effects of the voltage and current distortion on the equipment that can be economically quantified are the energy losses, the premature aging and the misoperation [6]. The evaluation of the cost to the electric utility to contend with the harmonic pollution is the first contributions [44, 45]. The costs include the total active power losses value as well as the capital invested in the design and construction of filtering system and recognized the cost due to premature aging cost of the equipment as potential additional cost but it was not include in this cost estimation. In [22, 23] the cost due to harmonic was extended to take into account also the premature aging of the equipment and the operating cost. A simplified approached base on closed form relation was proposed to evaluate the above quantities but it can be applied when considering only one group of nonlinear load is the main cause of the harmonic pollution. The operating costs are referred to the cause of incremental energy losses cause by harmonic flow in each component but the incremental cost of demand lost are not taken into account. The aging costs are referred to incremental of investment cost cause by premature aging of components due to harmonic pollution. The procedure steps needed to compute the cost of energy losses can be found in [4, 44, 45] for a distribution system and in [22, 23] for the industrial system also referring the probabilistic scenario.
To evaluate the cost of the additional energy losses and the aging cost arising for the system life period it is required the knowledge of system operating conditions in the study period network configurations and a typical duration of system states, the knowledge of type, operating conditions and absorbed power level of linear and non linear loads, the knowledge of life models of equipment and components to estimate the failure times of their electrical insulation and the assignment of the buying costs of the components together with their variation rate [35]. For estimating the aging costs in presence of statistically characterized harmonics the procedure is described in [22, 23] referring to cases in which the thermal stress is prevailing.
The system operating costs and the aging costs increase with the harmonic pollution and with a law dependent on the type and on the size of equipment [6]. In particular the aging costs can assume not negligible values of high levels of harmonic pollution also in case of only the thermal stress. For a practical quantification of the misoperation cost, it can be also introduced the concept of "mission-quality" of the equipment, for example the quality of the equipment performance that can be compromised by harmonics that, together with a measurable "quality performance figure", can allow the computation of the misoperation economical damage [6]
Transformer Losses and Lost of Life Calculation.
Transformer losses are generally classified into no load losses and load losses as shown in (1) [2, 3, 10, 18, 24, 47, 49].
(1)
Where,
PT = total loss, watt
PNL = no load loss, watt
PLL = load loss, watt
The no load loss or excitation loss are the losses due to the voltage excitation of the core and are due to magnetic hysteresis and eddy currents. The load loss or impedance loss is subdivide into I2R loss and stray loss caused by electromagnetic flux in the winding, core, core clamps, magnetic shield, enclosure or tanks walls, etc [2, 3].
(2)
Where,
PI2R = loss in the winding
PEC = eddy current loss
POSL = other stray loss
Loss in the winding can be obtained as follows [18]:
(3)
Where,
In = current of harmonic order n
Rn = resistance at harmonic frequency
The total eddy current loss including harmonic frequency component, can be calculated by (4) [10, 11, 49].
(4)
Or by (5) [24]
(5)
The total stray loss can be calculated as follow [10]:
(6)
Or [18]
(7)
Where,
PEC-R = rated winding eddy current losses
PEC1 = fundamental winding eddy current losses
POSL1 = fundamental other stray loss
POSL-R = rated other stray loss
In = harmonic current component magnitude
I1 = fundamental current
IR = transformer rated current
n = harmonic component
The evaluation of power transformers loss of life is highly dependent of deterioration conditions of the materials [51, 52]. Several studies on power transformer loss of life have been made [7, 50, 51, 52, 53]. About 50% of a transformer loss of life is caused by thermal stresses which are produced by the non-linear load current [51]. To relate the transformer loss of life with the temperature the Arrhenius/ Dakin expression used as follows [50, 51].
(8)
Where,
L% = transformer loss of life in per cent.
T = duration time, in hours, of the transformer loading
θe = hottest spot temperature in °C
A = empirical value, that represent the windings temperature increment, related to the ambient temperature;
- if the temperature increment is of 65°C then A = -13.391
- if the temperature increment is of 45°C then A = -14.133
The θe, can be calculated as shown in reference [50].
Cable Losses and Lost of Life Calculation.
The losses due to distorted current are basically proportional to the square of rms current [9, 10, 11, 13]. The following equation is shown if the resistance increase with the frequency due to skin and proximity effect is taken into account [10, 11].
(9)
If only the resistance at fundamental frequency is considered and the increased with frequency are neglected, the losses due to distorted current is as follows [10].
(10)
Both fundamental reactive and harmonic losses can be added and define as a single quantity called total reactive I2R loss, measured in watt and presented by Preactive.
(11)
(12)
Where,
Pj = total I2R loss
In = current of harmonic order n
I1 = fundamental current
R1 = ac resistance at fundamental frequency
Rn = ac resistance at harmonic frequency
P1 = I2R loss due to the fundamental current
Ph = I2R loss due to the harmonic current
P1p = I2R loss due to the fundamental active current
P1q = I2R loss due to the fundamental reactive current
The thermal degradation in electric devices is mainly caused by temperature rise beyond the rated value. The loss of useful life can be estimated by using the Arrhenius expression [9, 54]:
(13)
Where,
dλ/dt = life expectancy variation
A = material constant
k = Boltzmann constant
θ = Boltzmann constant
E = activation energy of the aging reaction
The equation (13) is possible to verify the relationship between temperature rise and cable loss of life. To provide a manner of calculating the cable life expectancy for operating temperature other than rated one the following equation is most suitable [9, 54].
(14)
Where,
λ = lifetime referred to θ = θrat + Δθ;
λrat = rated lifetime referred to θ = θrat;
Δθ = temperature rise in relation to θrat in Celsius;
θrat = cable rated temperature in Kelvin.
Research Question
How to estimate the harmonic losses in the cables and transformers?
What are the THD at the distribution cable and the substation transformer in Peninsular Malaysia?
What are the cost of harmonic events and the impact of the events on customers?
What is the relevant of harmonic emission limit to the cost?
How many time cables and transformers are reported by TNB with age premature?
How to calculate the costs of harmonic regarding to the energy losses, premature aging and the misoperation of the transformer and cable.
What are the variations in harmonic distortion levels in Peninsular Malaysia distribution system as a function of the time of year?
What are the changes in harmonic distortion levels in Peninsular Malaysia distribution system over time (e.g. month, years)?
What are the impacts of Malaysian standards and IEC standard on harmonic events in Malaysia?
How much the deviation from the reference standard will affect the power system equipment especially cables and transformers.
What are the estimated cost-benefits of various mitigation strategies for the various industrial sectors in Peninsular Malaysia?
How to manage the harmonic in Peninsular Malaysia?
Objectives
To model and simulate harmonic losses in transformer and cable in low voltage distribution system in Peninsular Malaysia.
To estimate the losses and the cost of harmonic problems in the substation transformer and distribution cable.
To determine the relevant of harmonic emission limit with the cost.
To estimate cost-benefit of various mitigation strategies for the various industrial sectors in Malaysia
Scope
Measurement at the low voltage distribution network in Peninsular Malaysia ( 11kV -33kV)
Estimate the losses in distribution cable and substation transformer.
Survey/measurement - Industries which most reported/suspected harmonic events'
Economic evaluation on harmonic effect on transformers and cables
Use Malaysian standard and IEC standard to be compared in these finding
