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Considerations on hosting capacity for harmonic distortions on transmission and distribution systems
Electric Power Systems Research 119 (2015) 199–206
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Considerations on hosting capacity for harmonic distortions on transmission and distribution systems ´ b , Pedro M. Almeida c , Math H.J. Bollen d , Paulo F. Ribeiro e Ivan N. Santos a,∗ , Vladimir Cuk a
Federal University of Uberlândia (UFU), Brazil Eindhoven University of Technology (TU/e), The Netherlands c Federal University of Juiz de Fora (UFJF), Brazil d Luleå University of Technology (LTU), Sweden e Federal University of Itajubá (UNIFEI), Brazil b
a r t i c l e
i n f o
Article history: Received 21 May 2014 Received in revised form 18 September 2014 Accepted 19 September 2014 Keywords: Distributed generation Harmonic distortion Hosting capacity Power quality Power-system harmonics Renewable generation
a b s t r a c t The increasing penetration of renewable/distributed sources with non-linear characteristics demands a clear methodology for determining the amount of generation which can be connected to the system without deteriorating the performance (the hosting capacity). This paper proposes a methodology for determining the hosting capacity regarding harmonic distortions. The method includes aggregation effects of harmonic currents, the influence of harmonic distortion limits and harmonic generation profile. To exemplify an application of the proposed procedure, a simple case study is performed and analyzed. © 2014 Elsevier B.V. All rights reserved.
1. Introduction The worldwide increase in electric power generation based on distributed renewable energy sources, such as wind and solar power, has concerned the grid operators regarding their impact on the electric power system. This integration is one of the most important challenges for the future power system. The amount of new distributed energy sources that may be connected to a network depends on several factors. The characteristics of the generation units, electric parameters of the local network, regional normative requirements, load capacity, etc., should be taken into account [1]. The maximum amount of dispersed generation that can be supported by the network in a specific point of distributed system is called hosting capacity [2]. In other words, the hosting capacity is the greatest amount of distributed generation (DG) which can be connected to this singular point before a particular performance limit level is reached [3,4]. The term hosting capacity is mainly related to the DG integration issue. Nowadays it is an important matter for several areas in
∗ Corresponding author. Tel.: +55 34 3239 4732; fax: +55 34 3239 4704. E-mail address: [email protected] (I.N. Santos). http://dx.doi.org/10.1016/j.epsr.2014.09.020 0378-7796/© 2014 Elsevier B.V. All rights reserved.
electric power system. Different indicators may restrict the maximum amount of DG which can be connected to the system, such as: over-voltages, under-voltages, harmonics, voltage unbalances, overloading, etc. The curve with the generic relation between the performance index and the amount of dispersed generation is shown in Fig. 1, where the concept of the hosting capacity is illustrated [5]. Distributed generation like wind-turbines and photovoltaic (PV) panels typically use power-electronic converters as an interface to the grid. Therefore, they are potential sources of harmonic currents [2]. The non-sinusoidal injected current may increase voltage distortion in the network to inappropriate values. In this context, the harmonic hosting capacity can be defined as the maximum amount of DG which can be connected to the network without exceeding the harmonic distortion limit for each harmonic component. There are some studies aiming to determine the specific hosting capacity based on the under and over-voltage deviations [e.g., 1, 6] or on the overloading [7]. In this context, few of them address hosting capacity in terms of harmonic constraints [8–11]. In [8,9], a method for estimating the number of distributed energy resources with power-electronic interface that can be connected to a low-voltage network without exceeding acceptable distortion levels is presented. This approach can be applied specifically in the
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Fig. 1. Generic performance index versus the amount of dispersed generation. Fig. 3. Norton equivalent circuit for harmonic order h.
frequency range from 2 kHz to 9 kHz. Additionally, in [10,11] a study that explores the impact of harmonic regulations on the capacity of distribution networks to host DG is performed. This effort incorporates harmonic voltage constraints into an established optimal power flow planning method. The optimal power flow has traditionally been used for economic dispatch [12,13]. These studies focus on how to maximize the hosting capacity avoiding costly network upgrades [11], but they are not able to calculate the hosting capacity. Therefore, despite the fact that hosting capacity for harmonics has been mentioned in the reported researches, a methodology to calculate the harmonic hosting capacity has not yet been defined. Recently, a task force on DG, planning, and optimization, organized by some IEEE committees like PSPI (Power System Planning and Implementation), PSACE (Power System Analysis, Computing and Economics), and others, enumerates a large number of articles regarding the problematic of DG integration into transmission system [14]. Furthermore, the same reference has pointed out that the studies about net capacity and DG impact on transmission system still represent a challenge ahead. In this context and taking into account the aforementioned considerations, the current paper aims to propose a specific procedure for assessment of harmonic hosting capacity which can be applied to distribution or transmission networks. In Fig. 2, the behavior of this specific indicator is depicted. In this graphic, the background distortion is the existing harmonic distortion at the evaluating point and the distortion limit is the maximum harmonic distortion allowed for this particular point of the system. This limit depends on the local grid requirements. Additionally, it is important to highlight that the shape of the curve of this graphic is generic, in practice it strongly depends on the DG harmonic phase angles (aggregation effects), and impedances in the network.
The paper is structured as follows: In Section 2, the harmonic hosting capacity methodology for assessment of the grid performance is shown. In Section 3, a case study aiming to exemplify the application of the proposed methodology is addressed. Section 4 discusses additional aspects related to aggregation effect, influence of harmonic source profiles, and impact of harmonic voltage limits. Finally, Section 5 draws some general conclusions. 2. Harmonic hosting capacity assessment In order to estimate the harmonic hosting capacity, one or more quality indicators need to be calculated as a function of the installed capacity and compared with a predefined limit. In this context, to obtain a suitable indicator and threshold the following information is needed: • requirements on voltage distortion set by the regulator or in other international documents/codes; • the consequences of exceeding the threshold and the amount of risk the network operator is willing and/or allowed to take. When this information is available, the calculation becomes a matter of applying circuit-theory. In addition, it is worth mentioning that although the previously defined hosting capacity is expressed in terms of amount of (new) generation in Figs. 1 and 2, in this section the harmonic hosting capacity is presented in terms of (additional) harmonic current. The maximum number of units to be connected can be calculated taking into account the aggregation effects as discussed in the following sections. 2.1. The assessment procedure
Fig. 2. Harmonic distortion versus the amount of dispersed generation – a generic dependency.
Assuming a particular instant of electric system under analysis, a generic situation for harmonic distortion of order h can be considered using the Norton equivalent circuit exhibited in Fig. 3. In this figure, Z˙ u-h is the equivalent harmonic impedance of the utility system of order h, I˙ u-h is the equivalent harmonic current of order h produced by the utility system, and V˙ u-h is the harmonic voltage of order h at the utility busbar. The background distortion (V˙ u-h ) is due to the harmonic distortions from the same voltage level and also from upstream and downstream networks. If the connection point has no previously existing harmonic content (busbar without background distortion), the values of V˙ u-h and I˙ u-h will be null. This is a particular case of this generic procedure. The harmonic hosting capacity is defined as the maximum value of harmonic current of order h that will drive the harmonic voltage to a boundary of maximum acceptable distortion. Defining Vlimit-h
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as the maximum harmonic voltage value, the harmonic hosting capacity for the h order can be calculated by the following equation: |(I˙ u-h + I˙ HC-h ) · Z˙ u-h | = Vlimit−h
(1)
where, I˙ HC-h is the harmonic current hosting capacity of order h. This means that the boundary for harmonic voltage of order h will be reached when the current I˙ HC-h is injected into this busbar. Assuming that I˙ u-h = Iu-h ⭿˛, and I˙ HC-h = IHC-h ⭿ˇ, IHC-h can be written as:
IHC-h = −Iu-h . cos(˛ − ˇ) +
2 .[cos2 (˛ − ˇ) − 1] + Iu-h
V
limit−h
2
Zu-h (2)
where, Zu-h is the absolute value of impedance Z˙ u-h . The minimum value for harmonic hosting capacity, which is the worst case scenario, is obtained when the current injected into busbar has the same phase angle as harmonic distortion from the utility system, that is, ˛ − ˇ = 0◦ . In other words, in this case any new harmonic current injected into this busbar will raise the magnitude of voltage harmonic for this harmonic order at this point. Consequently, the magnitude of harmonic hosting capacity (IHC-h ) can be calculated for this case by (3). IHC−h = −Iu−h +
Vlimit−h Zu-h
(3)
Additionally, the maximum value for harmonic hosting capacity (best situation) happens when the phase angle ˛ opposes the phase angle ˇ, that is, ˛ − ˇ = 180◦ . Eq. (4) represents this situation. IHC-h = Iu-h +
Vlimit−h Zu-h
(4)
For both case scenarios (worst and best), it is not necessary to know the phase angles of the harmonic currents injected into the busbar. Nevertheless, only a range in hosting capacity can be calculated, where (3) and (4) give the lower and upper limit respectively for this range. Note that the range is larger for increasing background distortion and symmetrical around the hosting capacity for zero background distortion. To perform this assessment, it is necessary to know the approximate value of equivalent harmonic impedance of the utility system. This can be estimated applying specific methodologies and measurements. Several publications in the literature address this issue [15–20]. In this work, such procedures will not be explored. It is also important to notice that this approach aims the hosting capacity assessment in terms of individual voltage harmonics. The hosting capacity due to the total harmonic distortion (THD) limits will be discussed in Section 4 of this paper. 2.2. The complete procedure to worst and best case scenarios assessment For worst and best situations, the following procedure should be applied for each harmonic order h:
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is null (or very close to null, e.g. for higher order harmonics), this current is zero; 5. from the source impedance and the background distortion, calculate the magnitude of harmonic hosting capacity of order h (IHC-h ) for worst situation using (3) and for the best situation using (4); 6. from the emission per unit and the aggregation law, calculate the maximum number of units or maximum installed capacity as explained in the following sections. If the phase angles of currents (˛ and ˇ) are available for the assessment, a better harmonic hosting capacity estimation can be found using the aforementioned equation (2). Sometimes, this might be required to make the study less conservative. 2.3. Taking into account the electric network variations In order to perform this calculation in a real network for a long or a short period, a certain amount of data has to be available. This is due to the several variations that can be found in this system, such as: background distortion changes and modifications of harmonic network impedance. This dynamic behavior is very common in power system due to different factors, as: load variations, capacitor and transformer switching, and changes of harmonic injection as a consequence of non-linear loads and DGs. In this situation, to calculate the emission as a function of the installed capacity, the following information is needed: • existing values of the background distortion (voltage magnitude and phase angle), its daily, weekly and seasonal variations and expected changes in the near future; • emission from the new device or installation (solar or wind power installation in this case, but the same approach holds for other types of equipment): harmonic current, its daily, weekly and seasonal variations and any correlations with the background distortion; • source impedance as a function of the frequency, and any variations in source impedance. Once this information is available, it is possible to determine the hosting capacity by means of the proposed procedure for an electric network even when its characteristics and its parameters are varying. For this assessment, the authors suggest application of one method proposed in IEC 61000-3-6 [21]. Such method uses aggregation exponents to solve the problem of a network with multiple time-varying sources of distortion. The IEC 61000-3-6 is a planning tool and so is the harmonic hosting capacity method. The exponents recommended in IEC 61000-3-6.can be used as an assumption if there is not enough data about the time variations of harmonic currents of considered DG. 3. Case study: a Brazilian distribution network
1. select a busbar and define the maximum voltage distortion or the 95/99% value (Vlimit-h ) together with the window over which the voltage distortion is obtained using information from local grid codes, standards and regulation; 2. determine the equivalent harmonic impedance of the utility system of order h (Z˙ u-h ); 3. measure the voltage harmonic distortion of busbar (V˙ u-h ) – harmonic voltage background distortion; 4. calculate the equivalent harmonic current of order h produced by the utility system side (I˙ u-h = V˙ u-h /Z˙ u-h ). If background distortion
The proposed procedure will be evaluated in this section by a simple case study. In this study, a real Brazilian power system is analyzed for a particular network operation condition. 3.1. Electric system parameters The single-line diagram of the evaluated system is shown in Fig. 4. Complementarily, in Tables 1–4 the parameters of this distribution network are presented at 60 Hz.
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Fig. 4. Case study: single-line diagram of a Brazilian distribution network.
The G1 is a hydroelectric generator while the others are wind power plants. In this case study, the hosting capacity is evaluated at the 138 kV busbar 3. The following harmonic orders are considered: 2nd, 3rd, 5th, 7th, 11th, and 13th. Table 1 Equivalent line parameters – case study. Line
Resistance ()
Inductance (mH)
Capacitance (F)
1 2 3 4 5 6 7 8 9 10 11
17.05 2.51 16.72 9.88 8.39 4.08 0.06 2.37 0.70 2.09 13.05
152.55 22.43 172.51 60.34 27.32 45.25 0.36 14.48 6.06 18.19 54.52
1.140 0.167 1.330 0.480 0.310 0.300 0.003 0.110 0.050 0.140 0.370
3.2. Methodology application and results In order to apply the methodology it is necessary to know the harmonic limits defined by local grid codes. In the current Brazilian grid code for distribution network [22] the limits of individual harmonic distortion for this voltage level (138 kV) are summarized in Table 5. Table 6 presents the estimated impedance values of bus 3, and Table 7 shows the background harmonic voltages at the same busbar obtained by simulation.
Table 3 Equivalent generator parameters – case study. Generator
Nominal voltage (kV)
Nominal power (MVA)
G1 G2 G3 G4
138 138 34.5 69
680 30 72 18
Table 2 Equivalent transformer parameters – case study. Transformer
Nominal power (MVA)
TAP (kV)
Inductive reactance pu (%)
T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11
60 60 12 6 1 12 60 12 12 5 44
138/69 138/69 69/34.5 34.5/13.8 34.5/13.8 69/13.8 34.5/138 69/13.8 69/13.8 69/13.8 69/13.8
15.50 15.60 6.17 8.15 5.60 4.64 13.33 6.15 6.15 6.01 8.11
Table 4 Equivalent load parameters – case study. Load
Active power (MW)
Reactive power (MVAr)
1 2 3 4 5 6 7 8 9
1.7 0.6 14.6 6.3 5.0 16.6 0 2.2 10.5
0.7 0.3 11.1 4.6 2.1 6.0 −1.1 0.3 4.9
I.N. Santos et al. / Electric Power Systems Research 119 (2015) 199–206 Table 5 Voltage harmonic limits from Brazilian grid code. Order
Vlimit-h (%)
2nd 3rd 5th 7th 11th 13th
1.0 2.0 2.5 2.0 1.5 1.5
harmonic order [23]. But due to the lack of actual wind-turbine information, a constant value of 2% is used for all frequencies. Each harmonic will set a separate upper limit for the size of the park. The lowest of these values, from all harmonic orders, sets the hosting capacity. In this way, for the worst case scenario the limit is set by the 7th harmonic (3.1 A), and for the best scenario it is set by the 3rd order (13.4 A), in accordance with Table 8. The hosting capacity for the worst case scenario is 37 MW because this power produces a fundamental current of 155 A and 3.1 A of the 7th harmonic (2% of 155 A). Complementarily, for best scenario the hosting capacity is 160 MW for the reason that this power leads to a fundamental current of 670 A and a 3rd harmonic of 13.4 A (2% of 670 A). Therefore, a range in hosting capacity has been found for this particular example. It is worth emphasizing that the correct ratio between the maximum permissible harmonic current (hosting capacity in Amperes) and the maximum-acceptable size of a wind-park (hosting capacity in MVA) depends on a number of factors, among others:
Table 6 Harmonic impedances busbar 3 – case study. Order
Zu-h (%) a
2nd 3rd 5th 7th 11th 13th
28.10 65.02 72.04 80.00 21.02 23.03
a
• the emission from individual turbines; • the aggregation between individual turbines.
Base values: 138 kV and 100 MVA.
Table 7 Harmonic voltage distortion busbar 3 – case study. Order
Vu-h (%) a
2nd 3rd 5th 7th 11th 13th
0.060 0.082 0.646 0.813 0.022 0.017
It is not possible to make general statements about this ratio based on existing knowledge of harmonic distortions. Ref. [23] presents values up to 0.8% of the fundamental current for the emission of individual harmonics by modern wind-turbines. Ref. [24] discusses aggregation and amplification. It is also important to mention that in spite of the fact that the present case study is performed only for six harmonic components, the proposed procedure can be applied to other harmonic orders when required.
This proposed procedure is applied regarding both extreme situations (worst and best scenarios) for the above-mentioned six harmonic orders. The results of harmonic hosting capacity assessment are presented in Table 8 for both highlighted situations. In this table, the harmonic hosting capacity is presented in terms of harmonic currents. If we take into account, for example, the 11th harmonic order, the maximum harmonic current that can be injected into busbar 3 in the worst situation is 29.1 A and in the best situation is 30.6 A. This means that such currents in each situation are able to drive the harmonic voltage of 11th order to reach the limit established by the Brazilian grid code, that is, 1.5% of voltage harmonic distortion. 3.3. Discussion and analysis of results In this section a brief analysis of these results will be performed. For illustrative purposes a value of 2% is chosen for the harmonic current, relative to the installed capacity, of each order for the windpark. That means that the wind park injects into the utility system 2% of harmonic current orders 2, 3, 5, 7, etc. It should be noted that it is more likely that this value will in reality be different for each
Table 8 Harmonic hosting capacity results busbar 3 – case study. Order
2nd 3rd 5th 7th 11th 13th
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Harmonic hosting capacity current IHC-h (A) Worst situation (lower limit)
Best situation (upper limit)
14.0 12.3 8.0 3.1 29.1 26.7
15.8 13.4 21.0 17.8 30.6 27.8
4. Additional considerations In order to find the true hosting capacity regarding harmonic distortions, other additional factors may be taken into account. The level of aggregation among the renewable sources, the characteristic harmonic distortion profile, and the harmonic distortion limits established by grid codes are some examples. This section intends to make a first discussion about such issues as well as the hosting capacity due to the THD limits. 4.1. The impact of harmonic currents summation To estimate the impact of a group of distorting loads or generators, it is important to know how their harmonic currents are combined due to the differences in the phase angles. If we look at a group of harmonic sources connected to a single busbar in the system, the summated current is usually lower than the arithmetic sum of their magnitudes. Both their magnitudes and phase angles vary in time, so it is very difficult to predict the sum in a particular moment of time. The changes are caused by the weather conditions which determine the generators powers, voltage harmonics present due to other non-linearities in the network, time changes of the system impedance, different technologies, etc. Technical standard IEC 61000-3-6 [21] recommends using the following formula for the estimation of a sum of harmonic currents: Ih,sum =
Ih,i
(5)
i
where is the summation exponent, Ih,sum is the summated harmonic current, and Ih,i are the individual harmonic components of the same order. The summation exponents for different orders are suggested in the same standard, given in Table 9.
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Table 9 Summation exponents suggested by IEC 61000-3-6.
h<5 5 ≤ h ≤ 10 h > 10
1.0 1.4 2.0
The suggested summation exponents give a generalized simplified approach; however, they do not describe the aggregation of harmonic currents for all types of devices well. Summation exponents should be re-examined for all DG types, to take into account the differences between their converters and operating conditions. For wind turbines, aggregation was analyzed based on computer simulations in [25]. It was found that the exponents from Table 9 can lead both to underestimation and overestimation of harmonic currents, depending on the configuration of the wind farm and assumed conditions of phase angle variation. For photovoltaic (PV) inverters, the aggregation of harmonic currents was analyzed by laboratory experiments and field measurements in [26–28]. In [26], the current of one inverter and the whole PV plant were measured on three sites, and it was found that the relation between the single inverter current and the total current yields a value of close to 1 for h ≤ 10, and close to 2 for h ≥ 17. It is important to notice that the lower order harmonics have significantly higher levels than the high order harmonics. Laboratory experiments and a filed measurement shown in [27] showed that the values from Table 9 lead to underestimation of harmonic currents for most harmonic orders. In [28], from a field measurement it was reported that had values between 1 and 1.2 up to the 21st order, without a monotonous dependency from h. The main reason why values from Table 9 are too optimistic for PV inverters is the dependency between the harmonic currents of individual inverters. As the input powers of all inverters are dependent on almost identical values of solar irradiance, all inverters operate in very similar conditions. However, when connected to different installations, their emission can be different due to different harmonic voltages on their terminals. As an example, the probability distribution functions of phase angles for the 5th harmonic current of five identical PV inverters and the total 5th harmonic current during one week of measurement are shown in Fig. 5. It is noticeable that currents of individual units cover a very similar range of phase angles, leading to an almost arithmetical summation. 0.06 Total PV1
0.05
PV2
5th harmonic current [A]
Harmonic Order h
0.5 0.4 0.3 0.2 0.1 0
0
2000
4000 6000 Time [min]
8000
Fig. 6. The magnitude of the 5th harmonic current of a PV inverter during one week.
For wind generators, results of such field measurements are currently not available. A correction of summation exponents for wind applications is a needed future work. 4.2. The influence of generation profile on the harmonic hosting capacity evaluation Another issue that can influence the analysis of harmonic hosting capacity is the fact that wind and PV generation are not constant during the day due to the changing weather conditions among other factors. The harmonic emission is not always equal to its maximum. If we define the harmonic emission of a generator based on the maximum emission, we might unnecessary overestimate the distortion levels for most of the time. Therefore, it is important to analyze the impact of the generation profile. As an example, the 5th harmonic current of a residential PV inverter during approximately one week of measurement is shown in Fig. 6, based on 10 min aggregated values. It is noticeable that the current has a maximal value close to 0.5 A, and that it lasts relatively short during the week. This depends significantly on the weather conditions. The cumulative distribution of this current is shown in Fig. 7, with the 95% and 99% probability levels indicated. Assuming that the maximal current corresponds to the maximal power of the inverter, we can notice that for 95% of the time the current is almost 20% lower. If we adopt 99% as the confidence level, the difference becomes very small. As the harmonic voltage limits of EN 50160 [29] are defined for 95% of the 10 min values, it should be possible to use a certain nonexceeded level for harmonic current as well instead of the maximal value, for example the 95% or 99% probability level. A certain safety margin should be kept, e.g. looking at the maximal yearly irradiance
PV3 0.04
PV4
0.5
0.03
5th harmonic current [A]
pdf
PV5
0.02
0.01
0 50
100
150 Phase angle [deg.]
200
250
Fig. 5. Probability distribution functions of phase angles for the 5th harmonic current; five PV inverters and their total harmonic current during one week.
0.4 0.3 0.2 0.1 0 40
50
60 70 80 Percentage of time [%]
90
100
Fig. 7. Cumulative distribution of the 5th harmonic current.
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of the geographical location (without the clouds). In the case of wind generators, the cumulative distribution of wind speeds should be used. Probability levels (e.g. 95% not exceeded) provide better information than the capacity factor, which represents the average production.
Nevertheless, for a good estimate of K˙ h , it is necessary to carry out a detailed study about the harmonic generation profile as well as the summation of harmonic currents for the type of DG that will be connected. Thus, more research work needs to be performed concerning this specific assessment.
4.3. The effect of voltage distortion limits on the harmonic hosting capacity assessment
5. Conclusion
The limits for harmonics established by standards and grid codes are essential to determine the harmonic hosting capacity at a specific connection point. An important subject to be discussed in relation to the harmonic hosting capacity is the impact of the voltage-distortion limit on the hosting capacity in terms of harmonic currents and in terms of installed capacity. In the EN 50160 [29], there are different values of individual harmonic voltages for each voltage level (high, medium, and low voltages). For each voltage level, a limit for THD and for each individual harmonic distortion is defined. Under normal operating conditions, during each period of 7 days, 95% of the 10 min mean RMS values of each individual harmonic voltage should be less than or equal to the value limit given in specific tables of this standard for each voltage level. Nevertheless, these specifications are different in standards and regulations around the world [30–32]. For example: the averaging window can have other values like 1 min, or 3 s; the limits can cover 99%, or even 100% of the time. This will further depend on the specific local grid code and planning levels used by the local network operator. However, most of the other uncertainties in measurement and calculation have been resolved by the introduction of IEC 61000-4-30 [33]. Even for a fixed individual voltage harmonic limit of, for instance, 5% of the nominal voltage, the above percentiles (95%, 99%, and 100%), and averaging windows (3 s, 1 min, and 10 minutes) will likely result in nine different values for the hosting capacity in terms of installed capacity. Therefore, additional considerations and studies are necessary regarding this specific approach. 4.4. Hosting capacity due to the THD limits Until now, the hosting capacity has been defined in terms of individual voltage harmonics. However, the THD limits can be exceeded even if no single limit is breached. It is feasible to calculate the hosting capacity due to the voltage THD limits but additional information is required. In this case, it is necessary to estimate the ratio (K˙ h ) between each individual harmonic current (I˙ w-h ) and the magnitude of fundamental current (Iw-fund ) produced by the DG. Thus, this assessment depends on the characteristics of DG that will be connected to the network. Eq. (6) expresses the mentioned ratio. K˙ h =
I˙ w-h Iw-fund
(6)
Each voltage harmonic distortion of order h (Vh ) can be calculated for the evaluated busbar by the following equation: Vh = |(I˙ u-h + K˙ h .lw-fund ) · Z˙ u-h |
(7)
Assuming that V1 is the magnitude of fundamental voltage at this busbar, the hosting capacity can be found by means of computing Eq. (8).
|(I˙ u-h + K˙ h .Iw-fund(HC) ).Z˙ u-h |2 = V1 · THDlimit
(8)
h
where Iw-fund(HC) is the hosting capacity in terms of fundamental current due to the maximum value of the total voltage harmonic distortion (THDlimit ) that is allowed.
This paper presents a proposal of a procedure for hosting capacity assessment concerning harmonic distortions on transmission and distribution systems. A mathematical development of a generic equation able to determine the hosting capacity for a specific point of the power system network was performed. Additionally, the worst case and best case scenarios were calculated based on simplified equations. Then, a case study was carried out where the procedure was applied in an actual power system from the Brazilian network. This case study demonstrated the simplicity of the method proposed. Furthermore, additional observations on the impact of summation of harmonic currents (aggregation effect), influence of harmonic generation profile, effect of voltage distortion limits, and a first consideration regarding hosting capacity assessment due to the THD limits were made. Acknowledgements This work was supported in part by Eindhoven University of Technology (TU/e), Federal University of Uberlândia (UFU), Luleå University of Technology (LTU), Federal University of Juiz de Fora (UFJF), Federal University of Itajubá (UNIFEI), CAPES (Proc. BEX 10105/12-3), and CNPq (Proc. 239445/2012-0/SWE). References [1] N. Etherden, Increasing the hosting capacity of distributed energy resources using storage and communication (PhD Thesis), Lulea University of Technology, Lulea, 2014. [2] M.H.J. Bollen, F. Hassan, Integration of distributed generation in the power system, in: IEEE Press Series on Power Engineering, Wiley-Blackwell, New York, 2011. [3] J. Deuse, S. Grenard, M.H.J. Bollen, EU-DEEP integrated project – technical implications of the hosting-capacity of the system for DER, Int. J. Distrib. Energy Resour. 4 (1) (2008) 17–34. [4] N. Jenkins, R. Allan, P. Crossley, D. Kirschen, G. Strbac, Embedded generation – IEE Power and Energy Series, Institution of Engineering and Technology, 2000. [5] M.H.J. Bollen, Y. Yang, Y. Hassan, Integration of distributed generation in the power system - a power quality approach, in: Int. Conf. on Harmonic and Quality of Power (ICHQP), Australia, 2008. [6] T. Stetz, F. Marten, M. Braun, Improved low voltage grid-integration of photovoltaic systems in Germany, IEEE Trans. Sustain. Energy 4 (2) (2012) 534–542. [7] D. Haesen, F. Minne, J. Driesen, M.H.J. Bollen, Hosting capacity for motor starting in weak grids, in: Int. Conf. on Future Power Systems, Leuven, 2005. [8] M.H.J. Bollen, F.J. Sollerkvist, The hosting capacity of distribution networks against high-frequency harmonics emitted by distributed energy resources, in: Int. Conf. on Harmonics and Quality of Power (ICHQP), Portugal, 2006. [9] M.H.J. Bollen, P.F. Ribeiro, E.O.A. Larsson, C.M. Lundmark, Limits for voltage distortion in the frequency range 2 to 9 kHz, IEEE Trans. Power Deliv. 23 (3) (2008) 1481–1487. [10] W. Sun, G.P. Harrison, S.Z. Djokic, Incorporating harmonic limits into assessment of the hosting capacity of actives networks, in: Int. Conf. on Electricity Distribution (CIRED), Lisbon, 2012. [11] W. Sun, G.P. Harrison, S.Z. Djokic, Distribution network capacity assessment: incorporating harmonic distortion limits, in: IEEE Power and Energy Society General Meeting, San Diego, 2012. [12] H.W. Dommel, W.F. Tinney, Optimal power flow solutions, IEEE Trans. Power App. Syst. 87 (10) (1968) 1866–1876. [13] C.J. Dent, L.F. Ochoa, G.P. Harrison, Network distributed generation capacity analysis using OPF with voltage step constraints, IEEE Trans. Power Syst. 25 (1) (2010) 296–304. [14] A. Keane, L.F. Ochoa, C.L.T. Borges, G.W. Ault, A.D.A. Rodriguez, R.A.F. Currie, F. Pilo, C. Dent, G.P. Harrison, State-of-the-art techniques and challenges ahead for distributed generation planning and optimization, IEEE Trans. Power Syst. 28 (2) (2013) 1493–1501. [15] A. Oliveira, J.C. Oliveira, J.W. Resende, M.S. Miskulin, Practical approaches for AC system harmonic impedance measurements, IEEE Trans. Power Deliv. 6 (4) (1991) 1721–1726.
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[16] G.D. Breuer, G. Addis, R.H. Lasseter, J.J. Vithayathil, HVDC-AC harmonic interaction, Part I: A.C. system harmonic model with comparison of calculated and measured data, IEEE Trans. Power App. Syst. 101 (3) (1982) 701–708. [17] G.D. Breuer, G. Addis, R.H. Lasseter, J.J. Vithayathil, HVDC-AC harmonic interaction, Part II: A.C. system harmonic model with comparison of calculated and measured data, IEEE Trans. Power App. Syst. 101 (3) (1982) 709–718. [18] A.A. Girgis, R.B. Mcmanis, Frequency domain techniques for modeling distribution or transmission networks using capacitor switching induced transients, IEEE Trans. Power Deliv. 4 (3) (1989) 1882–1890. [19] R.P. Stratford, Harmonic pollution on power systems - a change in philosophy, IEEE Trans. Ind. Appl. 16 (5) (1980) 43–67. [20] W. Xu, E.E. Ahmed, X. Zhang, X. Liu, Measurement of network harmonic impedances: practical implementation issues and their solutions, IEEE Trans. Power Deliv. 17 (1) (2002) 210–216. [21] IEC 61000-3-6, Electromagnetic compatibility (EMC)–Part 3-6: Limits–Assessment of emission limits for the connection of distorting installations to MV, HV and EHV power systems, 2008. [22] National Brazilian Agency of Electrical Power System (ANEEL), Procedures to Power Delivery in Brazilian Electrical Power System (PRODIST): Module 8–Power Quality. Brazil, 2010. [23] K. Yang, M.H.J. Bollen, E.O.A. Larsson, M. Wahlberg, Measurements of harmonic emission versus active power from wind turbines, Elect. Power Syst. Res. 108 (2014) 304–3014. [24] K. Yang, M.H.J. Bollen, L. Yao, Theoretical emission study of windpark grids: emission propagation between windpark and grid, in: Int. Conf. on Electrical Power Quality and Utilization (EPQU), Piscataway, 2011.
[25] F. Medeiros, D.C. Brasil, C.A.G. Marques, C.A. Duque, P.F. Ribeiro, Considerations on the aggregation of harmonics produces by large wind farms, in: Int. Conf. on Harmonic and Quality of Power (ICHQP), Hong Kong, 2012. [26] G. Chicco, J. Schlabbach, F. Spertino, Operation of multiple inverters in gridconnected large-size photovoltaic installations, in: Int. Conf. on Electricity Distribution (CIRED), Prague, 2009. [27] A. Constantin, R.D. Lazar, J. Dannehl, S.B. Kjær, M. Ibsch, Calculation of harmonic current content in PV power plants based on single inverter data, in: 1st Solar Integration Workshop, Aarhus, 2011. ´ [28] V. Cuk, J.F.G. Cobben, W.L. Kling, P.F. Ribeiro, Analysis of harmonic current summation based on field measurements, IET Generation, Transm. Distrib. 7 (12) (2013) 1882–1890. [29] Standard EN 50160, Voltage characteristics of electricity supplied by public distribution systems, 2008. [30] S. Bhattacharyya, S. Cobben, P.F. Ribeiro, W. Kling, Harmonic emission limits and responsibilities at a point of connection, IET Generation, Transm. Distrib. 6 (3) (2012) 256–264. [31] D. Brasil, F. Medeiros, P.M. Almeida, P.G. Barbosa, C.A. Duque, P.F. Ribeiro, Requirements for large photovoltaic power pants connected to the transmission system: considerations and comparisons, in: Proc. of the 2nd Latin America Conf. on Innovative Smart Grid Technologies (ISGT-LA), São Paulo, 2013. [32] 5th Benchmarking Report on Quality of Electricity Supply, Council of European Energy Regulators (CEER), 2011. [33] IEC 61000-4-30, Electromagnetic compatibility (EMC) – Part 4-30: testing and measurement techniques – power quality measurement methods, 2003.
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Considerations on hosting capacity for harmonic distortions on transmission and distribution systems ´ b , Pedro M. Almeida c , Math H.J. Bollen d , Paulo F. Ribeiro e Ivan N. Santos a,∗ , Vladimir Cuk a
Federal University of Uberlândia (UFU), Brazil Eindhoven University of Technology (TU/e), The Netherlands c Federal University of Juiz de Fora (UFJF), Brazil d Luleå University of Technology (LTU), Sweden e Federal University of Itajubá (UNIFEI), Brazil b
a r t i c l e
i n f o
Article history: Received 21 May 2014 Received in revised form 18 September 2014 Accepted 19 September 2014 Keywords: Distributed generation Harmonic distortion Hosting capacity Power quality Power-system harmonics Renewable generation
a b s t r a c t The increasing penetration of renewable/distributed sources with non-linear characteristics demands a clear methodology for determining the amount of generation which can be connected to the system without deteriorating the performance (the hosting capacity). This paper proposes a methodology for determining the hosting capacity regarding harmonic distortions. The method includes aggregation effects of harmonic currents, the influence of harmonic distortion limits and harmonic generation profile. To exemplify an application of the proposed procedure, a simple case study is performed and analyzed. © 2014 Elsevier B.V. All rights reserved.
1. Introduction The worldwide increase in electric power generation based on distributed renewable energy sources, such as wind and solar power, has concerned the grid operators regarding their impact on the electric power system. This integration is one of the most important challenges for the future power system. The amount of new distributed energy sources that may be connected to a network depends on several factors. The characteristics of the generation units, electric parameters of the local network, regional normative requirements, load capacity, etc., should be taken into account [1]. The maximum amount of dispersed generation that can be supported by the network in a specific point of distributed system is called hosting capacity [2]. In other words, the hosting capacity is the greatest amount of distributed generation (DG) which can be connected to this singular point before a particular performance limit level is reached [3,4]. The term hosting capacity is mainly related to the DG integration issue. Nowadays it is an important matter for several areas in
∗ Corresponding author. Tel.: +55 34 3239 4732; fax: +55 34 3239 4704. E-mail address: [email protected] (I.N. Santos). http://dx.doi.org/10.1016/j.epsr.2014.09.020 0378-7796/© 2014 Elsevier B.V. All rights reserved.
electric power system. Different indicators may restrict the maximum amount of DG which can be connected to the system, such as: over-voltages, under-voltages, harmonics, voltage unbalances, overloading, etc. The curve with the generic relation between the performance index and the amount of dispersed generation is shown in Fig. 1, where the concept of the hosting capacity is illustrated [5]. Distributed generation like wind-turbines and photovoltaic (PV) panels typically use power-electronic converters as an interface to the grid. Therefore, they are potential sources of harmonic currents [2]. The non-sinusoidal injected current may increase voltage distortion in the network to inappropriate values. In this context, the harmonic hosting capacity can be defined as the maximum amount of DG which can be connected to the network without exceeding the harmonic distortion limit for each harmonic component. There are some studies aiming to determine the specific hosting capacity based on the under and over-voltage deviations [e.g., 1, 6] or on the overloading [7]. In this context, few of them address hosting capacity in terms of harmonic constraints [8–11]. In [8,9], a method for estimating the number of distributed energy resources with power-electronic interface that can be connected to a low-voltage network without exceeding acceptable distortion levels is presented. This approach can be applied specifically in the
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Fig. 1. Generic performance index versus the amount of dispersed generation. Fig. 3. Norton equivalent circuit for harmonic order h.
frequency range from 2 kHz to 9 kHz. Additionally, in [10,11] a study that explores the impact of harmonic regulations on the capacity of distribution networks to host DG is performed. This effort incorporates harmonic voltage constraints into an established optimal power flow planning method. The optimal power flow has traditionally been used for economic dispatch [12,13]. These studies focus on how to maximize the hosting capacity avoiding costly network upgrades [11], but they are not able to calculate the hosting capacity. Therefore, despite the fact that hosting capacity for harmonics has been mentioned in the reported researches, a methodology to calculate the harmonic hosting capacity has not yet been defined. Recently, a task force on DG, planning, and optimization, organized by some IEEE committees like PSPI (Power System Planning and Implementation), PSACE (Power System Analysis, Computing and Economics), and others, enumerates a large number of articles regarding the problematic of DG integration into transmission system [14]. Furthermore, the same reference has pointed out that the studies about net capacity and DG impact on transmission system still represent a challenge ahead. In this context and taking into account the aforementioned considerations, the current paper aims to propose a specific procedure for assessment of harmonic hosting capacity which can be applied to distribution or transmission networks. In Fig. 2, the behavior of this specific indicator is depicted. In this graphic, the background distortion is the existing harmonic distortion at the evaluating point and the distortion limit is the maximum harmonic distortion allowed for this particular point of the system. This limit depends on the local grid requirements. Additionally, it is important to highlight that the shape of the curve of this graphic is generic, in practice it strongly depends on the DG harmonic phase angles (aggregation effects), and impedances in the network.
The paper is structured as follows: In Section 2, the harmonic hosting capacity methodology for assessment of the grid performance is shown. In Section 3, a case study aiming to exemplify the application of the proposed methodology is addressed. Section 4 discusses additional aspects related to aggregation effect, influence of harmonic source profiles, and impact of harmonic voltage limits. Finally, Section 5 draws some general conclusions. 2. Harmonic hosting capacity assessment In order to estimate the harmonic hosting capacity, one or more quality indicators need to be calculated as a function of the installed capacity and compared with a predefined limit. In this context, to obtain a suitable indicator and threshold the following information is needed: • requirements on voltage distortion set by the regulator or in other international documents/codes; • the consequences of exceeding the threshold and the amount of risk the network operator is willing and/or allowed to take. When this information is available, the calculation becomes a matter of applying circuit-theory. In addition, it is worth mentioning that although the previously defined hosting capacity is expressed in terms of amount of (new) generation in Figs. 1 and 2, in this section the harmonic hosting capacity is presented in terms of (additional) harmonic current. The maximum number of units to be connected can be calculated taking into account the aggregation effects as discussed in the following sections. 2.1. The assessment procedure
Fig. 2. Harmonic distortion versus the amount of dispersed generation – a generic dependency.
Assuming a particular instant of electric system under analysis, a generic situation for harmonic distortion of order h can be considered using the Norton equivalent circuit exhibited in Fig. 3. In this figure, Z˙ u-h is the equivalent harmonic impedance of the utility system of order h, I˙ u-h is the equivalent harmonic current of order h produced by the utility system, and V˙ u-h is the harmonic voltage of order h at the utility busbar. The background distortion (V˙ u-h ) is due to the harmonic distortions from the same voltage level and also from upstream and downstream networks. If the connection point has no previously existing harmonic content (busbar without background distortion), the values of V˙ u-h and I˙ u-h will be null. This is a particular case of this generic procedure. The harmonic hosting capacity is defined as the maximum value of harmonic current of order h that will drive the harmonic voltage to a boundary of maximum acceptable distortion. Defining Vlimit-h
I.N. Santos et al. / Electric Power Systems Research 119 (2015) 199–206
as the maximum harmonic voltage value, the harmonic hosting capacity for the h order can be calculated by the following equation: |(I˙ u-h + I˙ HC-h ) · Z˙ u-h | = Vlimit−h
(1)
where, I˙ HC-h is the harmonic current hosting capacity of order h. This means that the boundary for harmonic voltage of order h will be reached when the current I˙ HC-h is injected into this busbar. Assuming that I˙ u-h = Iu-h ⭿˛, and I˙ HC-h = IHC-h ⭿ˇ, IHC-h can be written as:
IHC-h = −Iu-h . cos(˛ − ˇ) +
2 .[cos2 (˛ − ˇ) − 1] + Iu-h
V
limit−h
2
Zu-h (2)
where, Zu-h is the absolute value of impedance Z˙ u-h . The minimum value for harmonic hosting capacity, which is the worst case scenario, is obtained when the current injected into busbar has the same phase angle as harmonic distortion from the utility system, that is, ˛ − ˇ = 0◦ . In other words, in this case any new harmonic current injected into this busbar will raise the magnitude of voltage harmonic for this harmonic order at this point. Consequently, the magnitude of harmonic hosting capacity (IHC-h ) can be calculated for this case by (3). IHC−h = −Iu−h +
Vlimit−h Zu-h
(3)
Additionally, the maximum value for harmonic hosting capacity (best situation) happens when the phase angle ˛ opposes the phase angle ˇ, that is, ˛ − ˇ = 180◦ . Eq. (4) represents this situation. IHC-h = Iu-h +
Vlimit−h Zu-h
(4)
For both case scenarios (worst and best), it is not necessary to know the phase angles of the harmonic currents injected into the busbar. Nevertheless, only a range in hosting capacity can be calculated, where (3) and (4) give the lower and upper limit respectively for this range. Note that the range is larger for increasing background distortion and symmetrical around the hosting capacity for zero background distortion. To perform this assessment, it is necessary to know the approximate value of equivalent harmonic impedance of the utility system. This can be estimated applying specific methodologies and measurements. Several publications in the literature address this issue [15–20]. In this work, such procedures will not be explored. It is also important to notice that this approach aims the hosting capacity assessment in terms of individual voltage harmonics. The hosting capacity due to the total harmonic distortion (THD) limits will be discussed in Section 4 of this paper. 2.2. The complete procedure to worst and best case scenarios assessment For worst and best situations, the following procedure should be applied for each harmonic order h:
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is null (or very close to null, e.g. for higher order harmonics), this current is zero; 5. from the source impedance and the background distortion, calculate the magnitude of harmonic hosting capacity of order h (IHC-h ) for worst situation using (3) and for the best situation using (4); 6. from the emission per unit and the aggregation law, calculate the maximum number of units or maximum installed capacity as explained in the following sections. If the phase angles of currents (˛ and ˇ) are available for the assessment, a better harmonic hosting capacity estimation can be found using the aforementioned equation (2). Sometimes, this might be required to make the study less conservative. 2.3. Taking into account the electric network variations In order to perform this calculation in a real network for a long or a short period, a certain amount of data has to be available. This is due to the several variations that can be found in this system, such as: background distortion changes and modifications of harmonic network impedance. This dynamic behavior is very common in power system due to different factors, as: load variations, capacitor and transformer switching, and changes of harmonic injection as a consequence of non-linear loads and DGs. In this situation, to calculate the emission as a function of the installed capacity, the following information is needed: • existing values of the background distortion (voltage magnitude and phase angle), its daily, weekly and seasonal variations and expected changes in the near future; • emission from the new device or installation (solar or wind power installation in this case, but the same approach holds for other types of equipment): harmonic current, its daily, weekly and seasonal variations and any correlations with the background distortion; • source impedance as a function of the frequency, and any variations in source impedance. Once this information is available, it is possible to determine the hosting capacity by means of the proposed procedure for an electric network even when its characteristics and its parameters are varying. For this assessment, the authors suggest application of one method proposed in IEC 61000-3-6 [21]. Such method uses aggregation exponents to solve the problem of a network with multiple time-varying sources of distortion. The IEC 61000-3-6 is a planning tool and so is the harmonic hosting capacity method. The exponents recommended in IEC 61000-3-6.can be used as an assumption if there is not enough data about the time variations of harmonic currents of considered DG. 3. Case study: a Brazilian distribution network
1. select a busbar and define the maximum voltage distortion or the 95/99% value (Vlimit-h ) together with the window over which the voltage distortion is obtained using information from local grid codes, standards and regulation; 2. determine the equivalent harmonic impedance of the utility system of order h (Z˙ u-h ); 3. measure the voltage harmonic distortion of busbar (V˙ u-h ) – harmonic voltage background distortion; 4. calculate the equivalent harmonic current of order h produced by the utility system side (I˙ u-h = V˙ u-h /Z˙ u-h ). If background distortion
The proposed procedure will be evaluated in this section by a simple case study. In this study, a real Brazilian power system is analyzed for a particular network operation condition. 3.1. Electric system parameters The single-line diagram of the evaluated system is shown in Fig. 4. Complementarily, in Tables 1–4 the parameters of this distribution network are presented at 60 Hz.
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Fig. 4. Case study: single-line diagram of a Brazilian distribution network.
The G1 is a hydroelectric generator while the others are wind power plants. In this case study, the hosting capacity is evaluated at the 138 kV busbar 3. The following harmonic orders are considered: 2nd, 3rd, 5th, 7th, 11th, and 13th. Table 1 Equivalent line parameters – case study. Line
Resistance ()
Inductance (mH)
Capacitance (F)
1 2 3 4 5 6 7 8 9 10 11
17.05 2.51 16.72 9.88 8.39 4.08 0.06 2.37 0.70 2.09 13.05
152.55 22.43 172.51 60.34 27.32 45.25 0.36 14.48 6.06 18.19 54.52
1.140 0.167 1.330 0.480 0.310 0.300 0.003 0.110 0.050 0.140 0.370
3.2. Methodology application and results In order to apply the methodology it is necessary to know the harmonic limits defined by local grid codes. In the current Brazilian grid code for distribution network [22] the limits of individual harmonic distortion for this voltage level (138 kV) are summarized in Table 5. Table 6 presents the estimated impedance values of bus 3, and Table 7 shows the background harmonic voltages at the same busbar obtained by simulation.
Table 3 Equivalent generator parameters – case study. Generator
Nominal voltage (kV)
Nominal power (MVA)
G1 G2 G3 G4
138 138 34.5 69
680 30 72 18
Table 2 Equivalent transformer parameters – case study. Transformer
Nominal power (MVA)
TAP (kV)
Inductive reactance pu (%)
T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11
60 60 12 6 1 12 60 12 12 5 44
138/69 138/69 69/34.5 34.5/13.8 34.5/13.8 69/13.8 34.5/138 69/13.8 69/13.8 69/13.8 69/13.8
15.50 15.60 6.17 8.15 5.60 4.64 13.33 6.15 6.15 6.01 8.11
Table 4 Equivalent load parameters – case study. Load
Active power (MW)
Reactive power (MVAr)
1 2 3 4 5 6 7 8 9
1.7 0.6 14.6 6.3 5.0 16.6 0 2.2 10.5
0.7 0.3 11.1 4.6 2.1 6.0 −1.1 0.3 4.9
I.N. Santos et al. / Electric Power Systems Research 119 (2015) 199–206 Table 5 Voltage harmonic limits from Brazilian grid code. Order
Vlimit-h (%)
2nd 3rd 5th 7th 11th 13th
1.0 2.0 2.5 2.0 1.5 1.5
harmonic order [23]. But due to the lack of actual wind-turbine information, a constant value of 2% is used for all frequencies. Each harmonic will set a separate upper limit for the size of the park. The lowest of these values, from all harmonic orders, sets the hosting capacity. In this way, for the worst case scenario the limit is set by the 7th harmonic (3.1 A), and for the best scenario it is set by the 3rd order (13.4 A), in accordance with Table 8. The hosting capacity for the worst case scenario is 37 MW because this power produces a fundamental current of 155 A and 3.1 A of the 7th harmonic (2% of 155 A). Complementarily, for best scenario the hosting capacity is 160 MW for the reason that this power leads to a fundamental current of 670 A and a 3rd harmonic of 13.4 A (2% of 670 A). Therefore, a range in hosting capacity has been found for this particular example. It is worth emphasizing that the correct ratio between the maximum permissible harmonic current (hosting capacity in Amperes) and the maximum-acceptable size of a wind-park (hosting capacity in MVA) depends on a number of factors, among others:
Table 6 Harmonic impedances busbar 3 – case study. Order
Zu-h (%) a
2nd 3rd 5th 7th 11th 13th
28.10 65.02 72.04 80.00 21.02 23.03
a
• the emission from individual turbines; • the aggregation between individual turbines.
Base values: 138 kV and 100 MVA.
Table 7 Harmonic voltage distortion busbar 3 – case study. Order
Vu-h (%) a
2nd 3rd 5th 7th 11th 13th
0.060 0.082 0.646 0.813 0.022 0.017
It is not possible to make general statements about this ratio based on existing knowledge of harmonic distortions. Ref. [23] presents values up to 0.8% of the fundamental current for the emission of individual harmonics by modern wind-turbines. Ref. [24] discusses aggregation and amplification. It is also important to mention that in spite of the fact that the present case study is performed only for six harmonic components, the proposed procedure can be applied to other harmonic orders when required.
This proposed procedure is applied regarding both extreme situations (worst and best scenarios) for the above-mentioned six harmonic orders. The results of harmonic hosting capacity assessment are presented in Table 8 for both highlighted situations. In this table, the harmonic hosting capacity is presented in terms of harmonic currents. If we take into account, for example, the 11th harmonic order, the maximum harmonic current that can be injected into busbar 3 in the worst situation is 29.1 A and in the best situation is 30.6 A. This means that such currents in each situation are able to drive the harmonic voltage of 11th order to reach the limit established by the Brazilian grid code, that is, 1.5% of voltage harmonic distortion. 3.3. Discussion and analysis of results In this section a brief analysis of these results will be performed. For illustrative purposes a value of 2% is chosen for the harmonic current, relative to the installed capacity, of each order for the windpark. That means that the wind park injects into the utility system 2% of harmonic current orders 2, 3, 5, 7, etc. It should be noted that it is more likely that this value will in reality be different for each
Table 8 Harmonic hosting capacity results busbar 3 – case study. Order
2nd 3rd 5th 7th 11th 13th
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Harmonic hosting capacity current IHC-h (A) Worst situation (lower limit)
Best situation (upper limit)
14.0 12.3 8.0 3.1 29.1 26.7
15.8 13.4 21.0 17.8 30.6 27.8
4. Additional considerations In order to find the true hosting capacity regarding harmonic distortions, other additional factors may be taken into account. The level of aggregation among the renewable sources, the characteristic harmonic distortion profile, and the harmonic distortion limits established by grid codes are some examples. This section intends to make a first discussion about such issues as well as the hosting capacity due to the THD limits. 4.1. The impact of harmonic currents summation To estimate the impact of a group of distorting loads or generators, it is important to know how their harmonic currents are combined due to the differences in the phase angles. If we look at a group of harmonic sources connected to a single busbar in the system, the summated current is usually lower than the arithmetic sum of their magnitudes. Both their magnitudes and phase angles vary in time, so it is very difficult to predict the sum in a particular moment of time. The changes are caused by the weather conditions which determine the generators powers, voltage harmonics present due to other non-linearities in the network, time changes of the system impedance, different technologies, etc. Technical standard IEC 61000-3-6 [21] recommends using the following formula for the estimation of a sum of harmonic currents: Ih,sum =
Ih,i
(5)
i
where is the summation exponent, Ih,sum is the summated harmonic current, and Ih,i are the individual harmonic components of the same order. The summation exponents for different orders are suggested in the same standard, given in Table 9.
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Table 9 Summation exponents suggested by IEC 61000-3-6.
h<5 5 ≤ h ≤ 10 h > 10
1.0 1.4 2.0
The suggested summation exponents give a generalized simplified approach; however, they do not describe the aggregation of harmonic currents for all types of devices well. Summation exponents should be re-examined for all DG types, to take into account the differences between their converters and operating conditions. For wind turbines, aggregation was analyzed based on computer simulations in [25]. It was found that the exponents from Table 9 can lead both to underestimation and overestimation of harmonic currents, depending on the configuration of the wind farm and assumed conditions of phase angle variation. For photovoltaic (PV) inverters, the aggregation of harmonic currents was analyzed by laboratory experiments and field measurements in [26–28]. In [26], the current of one inverter and the whole PV plant were measured on three sites, and it was found that the relation between the single inverter current and the total current yields a value of close to 1 for h ≤ 10, and close to 2 for h ≥ 17. It is important to notice that the lower order harmonics have significantly higher levels than the high order harmonics. Laboratory experiments and a filed measurement shown in [27] showed that the values from Table 9 lead to underestimation of harmonic currents for most harmonic orders. In [28], from a field measurement it was reported that had values between 1 and 1.2 up to the 21st order, without a monotonous dependency from h. The main reason why values from Table 9 are too optimistic for PV inverters is the dependency between the harmonic currents of individual inverters. As the input powers of all inverters are dependent on almost identical values of solar irradiance, all inverters operate in very similar conditions. However, when connected to different installations, their emission can be different due to different harmonic voltages on their terminals. As an example, the probability distribution functions of phase angles for the 5th harmonic current of five identical PV inverters and the total 5th harmonic current during one week of measurement are shown in Fig. 5. It is noticeable that currents of individual units cover a very similar range of phase angles, leading to an almost arithmetical summation. 0.06 Total PV1
0.05
PV2
5th harmonic current [A]
Harmonic Order h
0.5 0.4 0.3 0.2 0.1 0
0
2000
4000 6000 Time [min]
8000
Fig. 6. The magnitude of the 5th harmonic current of a PV inverter during one week.
For wind generators, results of such field measurements are currently not available. A correction of summation exponents for wind applications is a needed future work. 4.2. The influence of generation profile on the harmonic hosting capacity evaluation Another issue that can influence the analysis of harmonic hosting capacity is the fact that wind and PV generation are not constant during the day due to the changing weather conditions among other factors. The harmonic emission is not always equal to its maximum. If we define the harmonic emission of a generator based on the maximum emission, we might unnecessary overestimate the distortion levels for most of the time. Therefore, it is important to analyze the impact of the generation profile. As an example, the 5th harmonic current of a residential PV inverter during approximately one week of measurement is shown in Fig. 6, based on 10 min aggregated values. It is noticeable that the current has a maximal value close to 0.5 A, and that it lasts relatively short during the week. This depends significantly on the weather conditions. The cumulative distribution of this current is shown in Fig. 7, with the 95% and 99% probability levels indicated. Assuming that the maximal current corresponds to the maximal power of the inverter, we can notice that for 95% of the time the current is almost 20% lower. If we adopt 99% as the confidence level, the difference becomes very small. As the harmonic voltage limits of EN 50160 [29] are defined for 95% of the 10 min values, it should be possible to use a certain nonexceeded level for harmonic current as well instead of the maximal value, for example the 95% or 99% probability level. A certain safety margin should be kept, e.g. looking at the maximal yearly irradiance
PV3 0.04
PV4
0.5
0.03
5th harmonic current [A]
PV5
0.02
0.01
0 50
100
150 Phase angle [deg.]
200
250
Fig. 5. Probability distribution functions of phase angles for the 5th harmonic current; five PV inverters and their total harmonic current during one week.
0.4 0.3 0.2 0.1 0 40
50
60 70 80 Percentage of time [%]
90
100
Fig. 7. Cumulative distribution of the 5th harmonic current.
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of the geographical location (without the clouds). In the case of wind generators, the cumulative distribution of wind speeds should be used. Probability levels (e.g. 95% not exceeded) provide better information than the capacity factor, which represents the average production.
Nevertheless, for a good estimate of K˙ h , it is necessary to carry out a detailed study about the harmonic generation profile as well as the summation of harmonic currents for the type of DG that will be connected. Thus, more research work needs to be performed concerning this specific assessment.
4.3. The effect of voltage distortion limits on the harmonic hosting capacity assessment
5. Conclusion
The limits for harmonics established by standards and grid codes are essential to determine the harmonic hosting capacity at a specific connection point. An important subject to be discussed in relation to the harmonic hosting capacity is the impact of the voltage-distortion limit on the hosting capacity in terms of harmonic currents and in terms of installed capacity. In the EN 50160 [29], there are different values of individual harmonic voltages for each voltage level (high, medium, and low voltages). For each voltage level, a limit for THD and for each individual harmonic distortion is defined. Under normal operating conditions, during each period of 7 days, 95% of the 10 min mean RMS values of each individual harmonic voltage should be less than or equal to the value limit given in specific tables of this standard for each voltage level. Nevertheless, these specifications are different in standards and regulations around the world [30–32]. For example: the averaging window can have other values like 1 min, or 3 s; the limits can cover 99%, or even 100% of the time. This will further depend on the specific local grid code and planning levels used by the local network operator. However, most of the other uncertainties in measurement and calculation have been resolved by the introduction of IEC 61000-4-30 [33]. Even for a fixed individual voltage harmonic limit of, for instance, 5% of the nominal voltage, the above percentiles (95%, 99%, and 100%), and averaging windows (3 s, 1 min, and 10 minutes) will likely result in nine different values for the hosting capacity in terms of installed capacity. Therefore, additional considerations and studies are necessary regarding this specific approach. 4.4. Hosting capacity due to the THD limits Until now, the hosting capacity has been defined in terms of individual voltage harmonics. However, the THD limits can be exceeded even if no single limit is breached. It is feasible to calculate the hosting capacity due to the voltage THD limits but additional information is required. In this case, it is necessary to estimate the ratio (K˙ h ) between each individual harmonic current (I˙ w-h ) and the magnitude of fundamental current (Iw-fund ) produced by the DG. Thus, this assessment depends on the characteristics of DG that will be connected to the network. Eq. (6) expresses the mentioned ratio. K˙ h =
I˙ w-h Iw-fund
(6)
Each voltage harmonic distortion of order h (Vh ) can be calculated for the evaluated busbar by the following equation: Vh = |(I˙ u-h + K˙ h .lw-fund ) · Z˙ u-h |
(7)
Assuming that V1 is the magnitude of fundamental voltage at this busbar, the hosting capacity can be found by means of computing Eq. (8).
|(I˙ u-h + K˙ h .Iw-fund(HC) ).Z˙ u-h |2 = V1 · THDlimit
(8)
h
where Iw-fund(HC) is the hosting capacity in terms of fundamental current due to the maximum value of the total voltage harmonic distortion (THDlimit ) that is allowed.
This paper presents a proposal of a procedure for hosting capacity assessment concerning harmonic distortions on transmission and distribution systems. A mathematical development of a generic equation able to determine the hosting capacity for a specific point of the power system network was performed. Additionally, the worst case and best case scenarios were calculated based on simplified equations. Then, a case study was carried out where the procedure was applied in an actual power system from the Brazilian network. This case study demonstrated the simplicity of the method proposed. Furthermore, additional observations on the impact of summation of harmonic currents (aggregation effect), influence of harmonic generation profile, effect of voltage distortion limits, and a first consideration regarding hosting capacity assessment due to the THD limits were made. Acknowledgements This work was supported in part by Eindhoven University of Technology (TU/e), Federal University of Uberlândia (UFU), Luleå University of Technology (LTU), Federal University of Juiz de Fora (UFJF), Federal University of Itajubá (UNIFEI), CAPES (Proc. BEX 10105/12-3), and CNPq (Proc. 239445/2012-0/SWE). References [1] N. Etherden, Increasing the hosting capacity of distributed energy resources using storage and communication (PhD Thesis), Lulea University of Technology, Lulea, 2014. [2] M.H.J. Bollen, F. Hassan, Integration of distributed generation in the power system, in: IEEE Press Series on Power Engineering, Wiley-Blackwell, New York, 2011. [3] J. Deuse, S. Grenard, M.H.J. Bollen, EU-DEEP integrated project – technical implications of the hosting-capacity of the system for DER, Int. J. Distrib. Energy Resour. 4 (1) (2008) 17–34. [4] N. Jenkins, R. Allan, P. Crossley, D. Kirschen, G. Strbac, Embedded generation – IEE Power and Energy Series, Institution of Engineering and Technology, 2000. [5] M.H.J. Bollen, Y. Yang, Y. Hassan, Integration of distributed generation in the power system - a power quality approach, in: Int. Conf. on Harmonic and Quality of Power (ICHQP), Australia, 2008. [6] T. Stetz, F. Marten, M. Braun, Improved low voltage grid-integration of photovoltaic systems in Germany, IEEE Trans. Sustain. Energy 4 (2) (2012) 534–542. [7] D. Haesen, F. Minne, J. Driesen, M.H.J. Bollen, Hosting capacity for motor starting in weak grids, in: Int. Conf. on Future Power Systems, Leuven, 2005. [8] M.H.J. Bollen, F.J. Sollerkvist, The hosting capacity of distribution networks against high-frequency harmonics emitted by distributed energy resources, in: Int. Conf. on Harmonics and Quality of Power (ICHQP), Portugal, 2006. [9] M.H.J. Bollen, P.F. Ribeiro, E.O.A. Larsson, C.M. Lundmark, Limits for voltage distortion in the frequency range 2 to 9 kHz, IEEE Trans. Power Deliv. 23 (3) (2008) 1481–1487. [10] W. Sun, G.P. Harrison, S.Z. Djokic, Incorporating harmonic limits into assessment of the hosting capacity of actives networks, in: Int. Conf. on Electricity Distribution (CIRED), Lisbon, 2012. [11] W. Sun, G.P. Harrison, S.Z. Djokic, Distribution network capacity assessment: incorporating harmonic distortion limits, in: IEEE Power and Energy Society General Meeting, San Diego, 2012. [12] H.W. Dommel, W.F. Tinney, Optimal power flow solutions, IEEE Trans. Power App. Syst. 87 (10) (1968) 1866–1876. [13] C.J. Dent, L.F. Ochoa, G.P. Harrison, Network distributed generation capacity analysis using OPF with voltage step constraints, IEEE Trans. Power Syst. 25 (1) (2010) 296–304. [14] A. Keane, L.F. Ochoa, C.L.T. Borges, G.W. Ault, A.D.A. Rodriguez, R.A.F. Currie, F. Pilo, C. Dent, G.P. Harrison, State-of-the-art techniques and challenges ahead for distributed generation planning and optimization, IEEE Trans. Power Syst. 28 (2) (2013) 1493–1501. [15] A. Oliveira, J.C. Oliveira, J.W. Resende, M.S. Miskulin, Practical approaches for AC system harmonic impedance measurements, IEEE Trans. Power Deliv. 6 (4) (1991) 1721–1726.
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