Integration of large- scale PV plants in non-sinusoidal environments: Considerations on hosting capacity and harmonic distortion limits

Renewable and Sustainable Energy Reviews 82 (2018) 176–186

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Integration of large- scale PV plants in non-sinusoidal environments: Considerations on hosting capacity and harmonic distortion limits

MARK

⁎

Selcuk Sakara, Murat E. Balcia, , Shady H.E. Abdel Aleemb, Ahmed F. Zobaac a b c

Electric Power Engineering, Luleå University of Technology, 931 87, Skellefteå, Sweden 15th of May Higher Institute of Engineering, Mathematical and Physical Sciences, Helwan, Cairo, Egypt College of Engineering, Design & Physical Sciences, Brunel University London, Uxbridge, United Kingdom

A R T I C L E I N F O

A B S T R A C T

Keywords: Distributed generation Harmonic analysis Hosting capacity Optimization Passive filters Penetration Power quality PV systems Reactive power compensation Voltage support

Distributed generation (DG) penetration in a system may affect power quality, and energy efficiency, if it exceeds a particular value, known as the system's hosting capacity (HC). In this work, a comprehensive overview of hosting capacity and harmonic distortion limits is presented and discussed. The highest allowable penetration level of photovoltaic (PV)-based distributed generation units, hosted on typical industrial distribution systems, was analyzed in terms of the three power quality and energy efficiency performance parameters, namely bus voltage limits, line ampacities, and harmonic distortion limits. The analytical results show that the system's HC decreases with increase in utility side's background voltage distortion and load side's nonlinearity values. The HC level was affected more by the nonlinearity of the load side than by the utility side's background voltage distortion. Therefore, a single-tuned passive filter is suggested for maximizing the system's limited HC. Further, an optimization algorithm was developed to find simultaneously the system's HC and the parameters of the proposed filter, by considering the three performance parameters as constraints. The proposed filter design was found to attain a better level of HC than what can be obtained with a traditional filter design, based on current demand distortion minimization.

1. Introduction The consolidation of clean energy generation technologies with conventional centralized power generation technologies has led to the emergence of new practices in power generation. Integration of these improved forms of distributed generation (DG) into power system networks and deregulated energy markets [1,2] has its own problems and limitations. By definition, distributed power generation technologies are embedded small-scale on-site generation (OSG) sources of power. They can take many forms, such as solar photovoltaic (PV) arrays, wind turbine generators (WTG), small hydropower sources, fuel cells, biomass sources, and others [3]. In recent years, installation of inverter-based distributed generation (DG) units, particularly photovoltaic (PV) energy systems, has been rapidly increasing in the distribution networks, because they provide the right solution for dealing with energy efficiency and clean energy issues. However, if they are not properly sized, they may lead to some problems in the distribution systems, such as over and under voltages, excessive line losses, overloading of transformers and feeders, protection failure, and high harmonic distortion levels exceeding the international standards’ limits. These problems occur when the amount of DG units exceeds the ⁎

maximum permissible penetration level, that is when the system (or the feeder) exceeds its hosting capacity (HC) limit [4,5]. In the literature, several design strategies (objectives) are manipulated for optimal planning of DG units, such as power loss reduction [6], reactive power compensation [7], voltage profile enhancement [8], system security and reliability improvement [9], and for maximizing the DG penetration. Besides, the constraints of the formulated optimization problems can be grouped as voltage limitations, represented by voltage variation ranges (under and over voltage limits), current limitations, expressed by the allowable loading capabilities of the lines/ cables and transformers, and DG limitations, represented by their types, numbers, sizes, and economics. Various optimization techniques are used to solve these optimization problems [6–11]. Currently, extensive employment of nonlinear loads and large-scale grid-connected DG units has led to considerably distorted voltages and currents, because of their aggregated harmonic distortions. These distorted bus voltages and line currents may result in excessive losses and poor energy transfer efficiency or power factor [12,13]. In addition, harmonic pollution decreases the lifetime of different types of power system equipment, such as supply lines, transformers, power factor (PF) correction capacitors and induction motors [14]. Besides, it was

Corresponding author. E-mail addresses: [email protected] (S. Sakar), [email protected] (M.E. Balci), [email protected] (S.H.E. Abdel Aleem), [email protected] (A.F. Zobaa).

http://dx.doi.org/10.1016/j.rser.2017.09.028 Received 3 May 2017; Received in revised form 12 July 2017; Accepted 6 September 2017 1364-0321/ © 2017 Elsevier Ltd. All rights reserved.

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In the first part of this paper, a comprehensive overview of hosting capacity and harmonic distortion limits is presented and discussed. Further, the maximum penetration level of PV-based DG units, hosted on a distorted distribution system having both background voltage harmonic distortion and nonlinear loads, is determined as an optimization problem. The bus voltage limits, current carrying capability of

observed in [15] that, in the optimal DG sizing studies, power system harmonic limitations should be added to avoid negative impacts of harmonic distortion-related problems. Also, the maximum allowable values for individual and total harmonic distortion of PCC voltages and currents defined in the international standards such as IEEE Standard 519 and IEC 61000-3-2 [16,17] should be strictly met.

Fig. 1. Hosting capacity outlook in Australia. (a) HC control, (b) HC implementation stages, (c) HC map, and (d) Available HC data.

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harmonic-constrained DG capacities. Likewise, the results presented by [35] suggest that a harmonic mitigation filter be used to increase the DG penetration level to the maximum allowable extent. Similarly, a DG planning problem, based on maximization of DG penetration level, while satisfying the bus voltage rms limits and the IEEE 519 voltage harmonic limits, was solved for different loads and DG scenarios [36]. One of the principal conclusions of that study is that decentralization of DG capacity can be handled as an approach to achieve higher DG penetration levels. In [37], a new optimization method was introduced to calculate the DG penetration level for both utilities and customer simultaneously. The limitations of both harmonic and protection coordination constraints are considered in [38] to obtain the system-hosted capacity. In [39], the authors introduce a probabilistic method to minimize annual energy losses and mitigate harmonic distortion in distorted networks, considering all possible operating conditions of the DG units. In [40], the authors propose a phase-shifting approach to mitigate harmonics, supplied with converter-connected DG units. The results illustrate that the presented method can reduce harmonic distortion of both steady and continuous harmonic sources, which in turn can increase the DG penetration. In [26], the authors introduce the term, Harmonic-Constrained Hosting Capacity (HC-HC), to denote the HC of the system that can be determined by considering only the voltage harmonic distortion limits. They present a methodology to calculate HC-HC by considering the Norton equivalent harmonic model of the system. Moreover, they present the best and the worst conditions [41] of HC-HC, when harmonic currents, injected by utility and DG unit, are in the same and reverse directions, respectively. In [42], CIGRÉ WG: C6-24 investigated the HC of distribution feeders in different countries, and they reported that the problems resulting from high DG penetration increase and the DSOs’ should have a new simple, transparent, scalable, proven, and repeatable methodology to assess the new DG integration requests. In [27,43] passive filters are proposed, for the first time, to increase the hosting capacity of PV-based DG units. Planning for the optimal Ctype passive filter that can obtain maximum DG penetration was carried out, while complying with the harmonic limits and other conventional DG considerations. In the test case studied, the proposed filter design approach was shown to achieve higher DG hosting capacity than what can be achieved by using a traditional filter design approach. However, the effect of diversity on the analysis of PV power plants with N inverters is not investigated. In [44], the authors solve the problem of optimum size and placement of the inverter-based DG units and capacitor banks by considering voltage support and active/reactive power loss reduction. In [45], the authors further suggest selective elimination of the main causes affecting the power quality, such as harmonics, load asymmetry, and useless reactive power flow to allow an increase of the HC of the grid. It is clear that different passive methods have been applied for managing the grid-HC with equipment emitting distortion. Besides, different emerging active methods are underway, such as using enhanced inverter capabilities for reactive power control as well as using energy storage technologies to allow a further increase of the system's HC [46,47]. Lastly, different methodological choices can be realized to enhance the grid-HC such as reactive power control [48,49], voltage control [50], active power curtailment, energy storage technologies [51], network reconfiguration and reinforcement [52], and harmonic mitigation techniques [53]. However, knowing how the HC analysis will be used will significantly shape the methodological choices that can be made.

the supply lines, and the harmonic distortion limits are all taken into consideration as design constraints. In the optimization algorithm, the Newton-Raphson method is used to calculate the fundamental voltages and currents of the system, and the decoupled harmonic power flow (DHPF) to derive the non-fundamental harmonic voltages and currents. A typical distribution network that supplies industrial nonlinear loads is investigated to establish the validity of the proposed approach. The system under study is simulated for various cases of utility side's background voltage harmonic distortion and load side's nonlinearity to show the possible harmonic pollution effects on the system's HC. In the second part of the paper, a single-tuned passive harmonic filter is suggested as a harmonic mitigation device to maximize the system capacity and thus host more PV-based DG units. Accordingly, the optimal single-tuned filter design algorithm is accompanied by the HC assessment algorithm, which was developed to find the HC of the system under harmonically polluted voltage and current conditions. The genetic algorithm (GA) is used for solving the two nested optimization problems, because of its computational efficiency and rapid convergence to the global solution with acceptable accuracy [18]. Finally, a comparative study of the results of various simulation experiments, with and without compensation, is presented to show the advantages of adopting the proposed filter design approach for improving the system's HC, as compared to those of the conventional filter design, which aims at minimizing current demand distortion. 2. An overview of hosting capacity and harmonic distortion limits The HC of distribution systems for the DG units with electric power interfaces was investigated by many researchers and distribution system operators (DSOs) in recent years [5]. In [19,20] a clear definition of the HC and the methodologies to specify the impacts of increasing distributed energy resources penetration on power systems were presented. It was clearly recognized that new challenges are to be faced due to the increasing amount of DG. Determination of HC enables the stakeholder to quantify the impact of the DG units on the performance of the power system by using a set of assessment indices [21,22]. The selection of these indices depends on the points of interest, such as voltage profile [23], mains protection [24], ampacities of the lines, steady-state voltage violations and fast voltage variations [25], lowfrequency [26,27] and high-frequency harmonic distortion levels [28], and so forth. Fig. 1(a) shows an illustration of grid-HC control that can enable much higher penetrations of renewable resources. Fig. 1(b) shows an illustrated road map of HC implementation stages. Fig. 1(c) presents the most valuable locations in Australia to invest in renewables in order to drive further investment in renewables innovation [29], and Fig. 1(d) shows a recent data of managed and unmanaged HC data in different Australian towns [30]. This kind of data will certainly evolve over time, but knowing how the HC analysis will be used will significantly support facilitates knowledge sharing to eliminate barriers and accelerate the uptake of renewable energy. For HC determination, the DG penetration level is increased in intervals of 0–100%, and for each penetration level, the selected performance indices are calculated. If any of them exceeds its limits [20], then the DG penetration level is determined as the system's HC. Besides, a feeder's HC is not a single value, but a range of values; therefore, many HC values can be calculated. In [31,32] the importance of incorporating harmonic distortion limits into the HC assessment process are presented and discussed. In [33], different expressions were proposed to find the maximum permissible penetration levels of DG units, without violating the voltage harmonic distortion limits of radial distribution systems with different load patterns. In [34], it was demonstrated that PF correction capacitors might cause resonance hazards in systems with DG units, which implies that, by using harmonic filters (active, passive, or hybrid filters), harmonic resonance can be avoided while increasing the

3. Problem description In this study, the highest allowable PV-based DG unit penetration level (or the HC of the system for that kind of DG unit) is determined for 178

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where [Ih] and [Yh] are the current injection vector and the system's admittance matrix for the hth harmonic, respectively. 3.1.1. Modeling of the line, capacitor banks, and hybrid loads For the fundamental power flow and non-fundamental voltage calculations, the line and capacitor banks are modeled by considering their hth harmonic admittances. The hth harmonic admittances of the line and capacitor banks can be expressed thus: h y line =

1 h h Rline + jXline

(2)

h 1 y cap = hycap

(3)

Xhline

is the hth inductive reactance of the feeder, which is given as where hX1line, and y1cap is the fundamental harmonic admittance of capacitor banks. The hybrid loads are arranged as linear and nonlinear loads. For the hth harmonic, the linear loads are represented by a shunt combination of resistance and inductive reactance, which are calculated from the fundamental power flow data. Therefore, the admittance of the linear load is found as follows:

P QL ⎤ yldh linear = Kl ⎡ 1L 2 − j ⎢V h VL1 2 ⎥ ⎣ L ⎦

(4)

where, PL and QL denote the total rated active and reactive powers of the load, and Kl is a factor that represents the percentage of the linear part of the load to the full load. Likewise, Kl can be obtained as follows: (5)

K l = 1 − Kn

where Kn is the factor that represents the nonlinearity percentage of the load, which ranges from 0 to 1, depending on the loads' nonlinearity level. These factors (Kn, Kl) extend the working ability of parametric studies, including different hybrid loading schemes. The nonlinear load is represented by the well-known ''harmonic current source model [16]'', wherein the magnitude of the fundamental current of the nonlinear load (I1NL) is determined by using the fundamental power flow results, as shown below:

Fig. 2. The system under study.

the typical industrial distribution system, shown in Fig. 2, as a constrained optimization problem. The system comprises distorted utility side, consumer cable, hybrid commercial and industrial loads that consist of linear and nonlinear loads, a PV power plant with string inverters and a single-tuned passive harmonic filter. This study aims at providing an optimal design for the single-tuned filter to mitigate harmonic distortion in maximizing the system's HC. Thus, two optimization problems, combined with each other, will be simultaneously solved. The modeling and power flow analysis issues will have to be provided for the studied system. Hence, the formulation of the proposed optimization problem and its search algorithm will be presented.

1 INL = Kn ⎡ ⎢ ⎣

1 h INL = C (h) INL

=

(7)

where C(h) is a factor that represents the ratio of the hth harmonic current to the fundamental one. 3.1.2. Modeling of DG units In the literature, just as the nonlinear loads, the harmonic current source model [54] is generally considered to represent the DG harmonic emissions and is expressed thus:

DHPF has been used to determine the currents/voltages of the system for each harmonic order. It has been carried out in two stages: (i) running power flow analysis at the fundamental frequency, and (ii) determining the non-fundamental harmonic bus voltages, using the nodal equations for each harmonic order. In the fundamental frequency power flow, the voltage components at the supply frequency is found by using the conventional NewtonRaphson (NR) algorithm where the utility and load buses are modeled as slack and PQ buses, respectively. For load flow at the fundamental frequency, the DG units, especially the PV-based DG units, are assumed to generate only active power, because they are designed to operate at unity PF, as per the IEEE Standard 1547–2003 of their proper interconnection with electrical power systems. The hth harmonic nodal equation, which is used to find the hth harmonic bus voltage vector ([Vh]), can be written thus:

[I h]

(6)

For other harmonic frequencies higher than the fundamental frequency; the harmonic current of the nonlinear load at harmonic order h, IhNL, is given by

3.1. Modeling and power flow analysis of the system

[Y h][V h]

PL + jQL ⎤ VL1 ⎥ ⎦

h 1 IDG = CDG (h) IDG = CDG (h)

SDG VL1

(8)

where SDG indicates the fundamental apparent power of each DG source at a specific time, and CDG(h) is the hth harmonic signature of the DG, i.e. a factor that represents the ratio of the harmonic current IhDG to the fundamental current I1DG of the DG at the hth harmonic order. For multiple DGs, the sum of harmonic currents at each harmonic order will be used. 3.1.3. Modeling of the single-tuned filter Traditionally, in the power systems, shunt capacitor banks are employed for PF correction and voltage support. However, it is well known

(1) 179

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currents of the inverters can be affected by diversity, which means partial cancellation of their harmonic currents due to dispersion of harmonic current phase angles. In the literature, to represent the effect of diversity on the analysis of PV power plants with N inverters, the expression given in Eq. (12) is generally used:

ξ(hN ) =

I(hN ) h I(1) N

(12)

ζh(N)

is the hth harmonic summation ratio for N inverters and where ranges from 0 to 1. In the same expression, Ih(1) and Ih(N) denote the magnitude of the hth harmonic current injected by an individual inverter and the magnitude of the total hth harmonic current injected by all inverters, respectively. In this study, according to [59], the summation ratio is assumed as unity for low-order harmonics (h > 15) and as 0.5 for higher-order harmonics. On the other hand, the diversity effect should also be considered for the current harmonics of the PV power plant and the nonlinear load. In this case, according to IEC standard 61000-3-6, the expression given in Eq. (13) can be used to sum up the current harmonics injected by the PV power plant and the nonlinear load.

Fig. 3. Single-tuned passive filter: (a) Single-phase equivalent circuit of the single-tuned filter, (b) frequency response.

that they may result in amplification of voltage and current harmonics caused by the nonlinear loads due to electrical resonance. Therefore, passive and active harmonic filters are preferred for harmonic mitigation and PF correction under distorted voltage and current conditions [55,56]. Compared to the active filters, single-tuned passive filters are still the most used filters in the power quality (PQ) markets because of their simplicity, straightforward configuration, trouble-free maintenance, and low-cost [57]. Single-phase equivalent circuit and the frequency response of that kind of passive filter are shown in Fig. 3. According to Fig. 3(a), the hth harmonic equivalent impedance (ZhF) of the filter can be written as in Eq. (9), given below:

X ZFh = RFh + jXFh = RF + j ⎡hXLF − CF ⎤ h ⎦ ⎣

σ

h (Isum ) =

XCF ht2

(Ihsum)σ

is the resultant In Eq. (13), σ is the summation exponent, harmonic current from summation, and (Ihi)σ is the ith individual harmonic component of the inverter at hth harmonic. In addition, σ varies according to the harmonic order, as follows [17]:

if h < 5 ⎫ ⎧ 1, σ = 1.4, if 5 ≤ h ≤ 15 ⎨ ⎬ if h > 15 ⎭ ⎩ 2

(9)

ht XCF RF

(14) (Ihresultant)

Therefore, the resultant hth current can be calculated from the combination of the hth nonlinear load and the hth DG currents, as follows: h Iresul tan t =

σ

h σ (INL ) + (I(hN ) )σ

(15)

3.2. Formulation of the optimization problem

(10)

At the fundamental frequency, the inductive reactance has negligible value, as compared to the capacitive reactance; thus, the value of the capacitive reactance is mainly dependent on the desired fundamental harmonic reactive power compensation. The last component of the filter, RF, is used to control the quality factor (q) or the sharpness of tuning, and q can be expressed as shown below:

q=

(13)

i

It can be seen from Fig. 3(b) that the single-tuned filter's impedance attains its minimum at the tuning harmonic frequency (or harmonic order), because its inductive and capacitive reactance should be equal to each other for that frequency. Thus, it absorbs the harmonic currents around its tuning harmonic order (ht). The relation between fundamental values of the inductive (XLF) and capacitive (XCF) reactances can be written thus:

XLF =

∑ (Iih)σ

As mentioned earlier, the goals of the proposed optimization approach are to achieve the system's maximum HC level under harmonic distortion condition and to find the optimal design of the single-tuned filter that can realize this maximum HC level. And, this implies simultaneous sizing of the PV-based DG units and the filter parameters to maximize the system's HC by taking into account the constraints of both conventional HC (bus voltage rms limit, the current carrying capability limits of the lines, DG size and the desired PF range) and harmonic distortion (individual and total harmonic distortion limits stated in IEEE 519). It should be mentioned here that only a few studies were carried out earlier on HC determination, under harmonically distorted conditions. These studies considered only individual and total voltage harmonic distortion limits as the harmonic constraints for HC assessment, because their systems consisted of only DG units as nonlinear equipment, but no nonlinear loads, which introduce highly distorted currents. However, for this study, since the studied system has not only DG units, but also the nonlinear loads, both individual and total distortions of the voltage and current are collectively considered for optimization. Furthermore, in the literature, optimal passive filter design studies generally aim at minimizing total demand distortion and/or total voltage harmonic distortion, while satisfying the desired PF range and complying with the IEEE 519 limits for individual and total harmonic distortion. However, the filters of this study have dual tasks of harmonics mitigation and system's HC level improvement. Therefore, the objective function and constraints of the proposed optimization approach are accordingly

(11)

The single-tuned filters have a better harmonic mitigation capability than other types of passive filters. However, they may result in parallel resonance in the system. Therefore, during their design stage, it should be checked whether resonance risks are safely avoided or not. In addition, the voltage and the current of the filter elements should be checked after their sizing to avoid any detrimental increase in their rating, as compared to their fundamental rating. In this regard, the capacitor rms current, rms voltage, peak voltage, and apparent power should not exceed 135%, 110%, 120%, and 135% of their nominal values, respectively, as per the IEEE Standard 18–2012 [58] for continuous loading duties of shunt capacitors operating under non-sinusoidal conditions. 3.1.4. Harmonic current summation of the PV power plants with multiple inverters and nonlinear load PV power plants operated at MV and HV levels have a large number of identical inverters connected to the same PCC. The total harmonic 180

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operating conditions, which is defined as the rated line current in this study in order to give meaningful current harmonic distortion data regardless of the loading conditions.

formulated as shown below: 3.2.1. Objective function The objective function (OF) of the proposed optimization approach is maximization of the system's HC, as expressed in Eq. (16) below:

Max HC (XLF , XCF , q, N ) =

PPV 100 MVArated

3.2.5. Individual harmonic distortion (IHD) constraints According to IEEE 519, the hth harmonic line current (Ihline) and the hth harmonic load voltage (VhL) values, given in terms of their fundamental values (I1line and V1L), should be bounded as follows:

(16)

where HC denotes the peak instantaneous penetration level, expressed as the ratio of the load bus’ rated apparent power (MVArated) and the rated DG power (PPV). XLF, XCF, and q denote inductive reactance, capacitive reactance and quality factor of the filter, respectively. In addition to that, the power of the PV plant, PPV, can be expressed in terms of the integer multiples (N) of the smallest possible PV-DG size (Pind PV ), as follows: ind PPV = PPV N

IHDC (XLF , XCF , q, N ) =

IHDV (XLF , XCF , q, N ) =

It should be noted that peak instantaneous penetration level is the ratio of DG power to the load's rated power at a particular point in time. This definition is a suitable indicator for observing the consequences of the DG's hosted power on the system, from the power quality (PQ) perspective [60].

3.2.7. PF constraint The true PF measured at the PCC should be maintained in the acceptable range to increase the energy-transfer efficiency of the system, so that:

(18)

PF =

3.2.3. Line current capability constraint Considering the frequency dependency of the line resistance under non-sinusoidal conditions, the harmonic de-rating factor (HDF) should be employed to determine the current carrying limit of the line [62]. Since HDF should not exceed 1 p.u., the second constraint can be written thus:

∑ h≥2

h h Rline ⎡ Iline ⎤ ≤ 1.0 1 ⎢ 1 ⎥ Rline I ⎣ line ⎦

(19)

3.2.4. Harmonic distortion constraints The limits recommended in the IEEE Standard 519 should be considered for harmonic control in interconnected DG units with electrical power systems, especially those connected on feeders, supplying nonlinear loads. Therefore, according to IEEE 519, the total demand distortion of the line current (TDD) and the total harmonic distortion of voltage (THDV), measured at the point of common coupling (PCC), should be regarded as the constraints of the formulated optimization problem, as shown below:

TDD (XLF , XCF , q, N ) =

∑h > 1 V Lh VL1 h ∑h > 1 Iline

IMD

2

(24) (25)

In this section, the numerical data of the system under study is presented first and then the initial HC of the uncompensated main feeder is parametrically estimated under different levels of utility's background voltage distortion (UBVD) and load's nonlinearity levels, represented by Kn. Second, as regards the worst HC point, a singletuned passive filter is designed to properly evaluate the capability of the proposed simultaneous filter design approach. Finally, the results of the proposed filter design strategy, under various nonlinear conditions, are presented and discussed.

(20)

2

≤ TDDmax

h ∑h Iline

4. Simulation results and discussion

2

≤ THDVmax

2

In this study, the capacitor rating, in kvar, is formulated as an integer multiple of 100 kvar (three-phase), which is common in the industry. Hence, selection of the filter parameters (XCF, XLF, q), as also of the integer multiple (N) of the smallest possible PV-DG size (Pind PV ), which is considered as 100 kW, is formulated as a mixed integer optimization problem to maximize the system's HC, under distorted voltage and current conditions. Genetic algorithm (GA) is preferred to solve the formulated mixed integer optimization, because it is one of the common evolutionary methods that can accurately solve optimization problems with continuous and discrete variables, having nonlinear objectives and constraints, and can converge to the global solution within short computation time.

Ihline

THDV (XLF , XCF , q, N ) =

∑h V Lh

3.3. The search algorithm of the optimization approach

and represent the currents flowing through the line at the where fundamental and the hth harmonic orders, respectively, and R1line and Rhline are the line resistances at the fundamental and the hth harmonic orders, respectively I1line

h cos θh ∑h V Lh Iline

0.90 ≤ PF (XLF , XCF , q, N ) ≤ 1.0

2

1+

(23)

3.2.6. DG size constraint The active power produced by the DG units should not exceed a certain percentage of the total feeder load [27] to guarantee that the planned DG units reduce the active line losses. For this study, 100% penetration (1 p.u. at rated loading conditions) is taken as the upper limit of the total DG size, in line with the literature [6–9].

3.2.2. Bus voltage constraint The rms value of bus voltage (VL) should be within the permissible range, which is usually ± 5% of per unit (p.u.) nominal voltage value [61]. According to this range or limits of the bus voltage, the voltage rms constraint should be given as follows:

HDF (XLF , XCF , q, N ) =

V Lh ≤ IHDVmax VL1

(22)

where, IHDC and IHDV represent the individual harmonic distortion percentages of current and voltage, respectively, and IHDCmax and IHDVmax, their maximum allowable values.

(17)

0.95 ≤ VL (XLF , XCF , q, N ) ≤ 1.05

h Iline ≤ IHDCmax 1 Iline

(21)

where THDVmax and TDDmax are the maximum values permitted by IEEE 519 for THDV and TDD, respectively, and V1L and VhL are, respectively, the fundamental voltage and the hth harmonic voltage of the PCC bus. Also, IMD is the maximum demand current under normal

4.1. System description The system under study has 13.8 kV, 50 cycles per second sinusoidal 181

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Table 1 Harmonic content of the nonlinear load's current and supply voltage as a percentage of their fundamental current and voltage a. h

IhNL

IHDCmax

UBVD

IHDVmax

5 7 11 13 17 19 23 25 29

20.0 14.3 9.1 7.7 5.9 5.3 4.3 4.0 3.4

7.0 7.0 3.5 3.5 2.5 2.5 1.0 1.0 1.0

3.0 2.0 2.0 1.0 1.0 1.0 1.0 0.5 0.5

3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

a

All magnitudes are given as percentages of the fundamental values.

and balanced three-phase utility voltages, as shown in Fig. 2. It is considered as an infinite system. It has a symmetric three-phase distribution line, whose rated line-to-line voltage and current ratings are 13.8 kV and 314 A, respectively. The rated three-phase apparent power of the system is 7.5 MVA. Its hth equivalent series impedance Zhline represents the line, so that its resistance R1line and inductive reactance ×1line, at the fundamental frequency, are given as 0.855, and 1.165 Ω, respectively. The nonlinear load, which is a six-pulse DC drive load, is modeled using current injections at its characteristic harmonic orders, as given in Table 1 [63]. The same Table also presents harmonic contents of the utility-side's background voltage distortion, as also the individual harmonic limitations of the PCC voltage (IHDVmax) and current (IHDCmax), recommended in the IEEE Standard 519–2014. In the same standard, the limits of voltage total harmonic distortion and total demand distortion, THDVmax and TDDmax, are defined, respectively, as 5% and 8% for the system under study. For harmonic signature of the DG units, the harmonic spectrum of a typical PV-based DG unit [64], at characteristic and non-characteristic harmonic orders, is provided in Table 2.

Fig. 4. Initial HC assessment of the system under study.

4.2. Uncompensated system results Initial appraisal of the system's HC is performed. Kn percentage is allowed to increase gradually from 0% to 25%, and UBVD percentage from 0% to 4.5%. For initial determination of the allowable size of the DG units with these Kn and UBVD intervals, the active power generated by the PV arrays (PPV) is permitted to increase gradually through small discrete steps until the constraints bounding the performance indices are violated. The flowchart in Fig. 4 demonstrates the initial assessment of the HC of the studied system. Using the proposed algorithm, the HC of the system, without passive filter (uncompensated system case), is determined for the considered Kn and UBVD intervals. The contour graph of the obtained HC results is given in Fig. 5. It can be seen from Fig. 5 that, under sinusoidal voltage condition,

Fig. 5. The HC results of the uncompensated system, obtained for the considered Kn and UBVD intervals.

Table 2 Harmonic content of a sample PV power plant with one inverter [64] b. h

Magnitude

h

Magnitude

h

Magnitude

1 2 3 4 5 6 7 8 9 10

100.0 1.13 3.27 0.26 3.48 0.12 1.12 0.82 0.49 0.84

11 12 13 14 15 16 17 18 19 20

0.67 0.80 0.46 1.06 0.30 0.50 1.48 0.59 1.14 0.71

21 22 23 24 25 26 27 28 29 30

0.50 0.40 0.20 0.35 1.33 0.19 0.61 1.20 0.90 0.67

b

i.e., UBVD = 0%, the HC value decreases to 50% for the highest Kn value, which is considered as 25%. Under linear loading condition, i.e., Kn = 0%, it is around 100% for the highest UBVD value, which is considered as 4.5%. The same figure also indicates that the UBVD value affects the HC level of the system considerably when the Kn value is higher than 10%. In addition, the uncompensated system has the lowest HC level, around 10%, for the highest Kn and UBVD values of 25% and 4.5%, respectively. Lastly, it can be inferred that Kn is the dominant parameter in HC aggregation, when compared to UBVD. For maximum penetration level of the DG, without violating its optimal sizing constraints, under the considered intervals of Kn and UBVD, the variations in THDV and TDD distortion levels, measured with the PCC, are shown in Fig. 6. It can be seen from Fig. 6 that both THDV

All magnitudes are given as percentages of the fundamental values.

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Table 3 Results of the simulated test cases. Parameter/case

THDV (%) TDD (%) PF (%) VL (p.u.) PLoss (kW) HDF (%) HC (%) PL (MW)

No-filter

5.34 6.07 82.52 0.94 288.30 99.47 – –

Compensated system Capacitor

Proposed

Traditional

7.55 23.12 96.20 0.97 216.75 93.95 – –

4.04 6.46 99.59 0.97 186.30 99.45 73.33 5.50

4.70 5.83 99.57 0.97 186.75 99.52 44.00 3.30

of hosting any PV power penetration. The same Table also shows that the PF, VL, PLoss and HDF values of the compensated system with shunt capacitor are 96.10%, 0.97 p.u, 216.75 kW, and 93.95%, respectively. Hence, it can be inferred that basic capacitive compensation improves these four parameters. However, for the same case, THDV and TDD are adversely affected, as they increase to 7.55% and 23.12%, respectively. It therefore follows that shunt capacitor does not contribute to any improvement of the system's HC level. The optimal parameters of the proposed filter design are found to be 1.72 p.u, 0.17 p.u, and 45 for the XCF, XLF, and q, respectively. Also, the number of used DG units (N) is determined as 55. It can be seen from Table 3 that the proposed filter design achieves THDV, TDD, PF, VL, PLoss and HDF values of 4.04%, 6.46%, 99.59%, 0.97 p.u, 186.30 kW, and 99.45%, respectively. For the compensated system with the proposed filter design, the penetration level (PL) of the PV plant is found to be 5.50 MW, and the system's HC level is determined as 73.33%. On the other hand, the optimal parameters of the conventional filter design are found to be 1.76 p.u, 0.36 p.u, and 20 for the XCF, XLF and q, respectively. Also, N is determined as 33. Also, Table 3 shows that the conventional filter design achieves THDV, TDD, PF, VL, PLoss and HDF values of 4.70%, 5.83%, 99.57%, 0.97 p.u, 186.75 kW, and 99.52%, respectively. For the compensated system with the conventional filter design, the PL of the PV plant is found to be 3.30 MW, and the system's HC level is determined as 44.00%. TThe impact of both single-tuned filter designs on the system's HC level is also tested. The contour graphs obtained from their performances under the test cases are shown in Fig. 7. It is evident that the proposed filter design attains a better level of HC than what can be obtained with the conventional filter design under all UBVD and Kn conditions.

Fig. 6. Results of the harmonic performance indices of the uncompensated system, obtained for the considered Kn and UBVD intervals: (a) THDV (%), (b) TDD.

and TDD are affected by UBVD and Kn variations. Moreover, Fig. 6(a) shows that THDV is close to its maximum permissible value (5%), recommended in the IEEE Standard 519 for Kn, and UBVD values are around 25% and 4.5%, respectively. Fig. 6(b) shows that TDD is close to its maximum permissible value (8%), recommended in the same standard of Kn for 15–25% intervals, under UBVD levels below 2.5%.

4.4. Harmonic penetration ratio (HPR) The goal of this study is to assess and improve the HC to the maximum allowable extent, under non-sinusoidal conditions. Unlike the sinusoidal system, the nonlinearity percentage of the load and the background voltage distortion limits of non-sinusoidal system affect the HC considerably, as has already been discussed under the results of the studied cases. Therefore, to assess the impact of harmonics on the HC, the maximum allowable DG capacity under non-sinusoidal conditions (PDGnl ) has to be calculated and compared to the maximum allowable DG capacity under sinusoidal conditions (PDGl ) , wherein the loads and the DG are harmonics-free. This can be represented using the proposed harmonic penetration ratio (HPR), defined in Eq. (26) as follows:

4.3. Compensated system results For UBVD and Kn values as 4.5% and 25%, respectively, the results of the uncompensated system are comparatively evaluated with those of the system compensated with the shunt capacitor and single-tuned filter. For shunt capacitive compensation, the reactance value of the capacitor is selected as 1.68 p.u. to provide PF of 95.00% at the PCC. On the other hand, two single-tuned filter designs are considered for the analysis. They are optimally designed for the proposed approach, which aims to maximize the system's HC level, and for the conventional approach, which aims to minimize the TDD percentage, considering the same constraints for the proposed and the conventional approaches. The simulated test results are shown in Table 3, from which it can be seen that the values of the uncompensated system for THDV, TDD, PF, VL, PLoss and HDF are 5.34%, 6.07%, 82.52%, 0.94 p.u, 288.3 kW, and 99.47%, respectively. Further, its HC level is nil, and is hence incapable

HPR =

PDGnl ≤1 PDGl

(26)

By definition, the HPR ratio ranges from 0 to 1; zero indicates that no DG penetration is available due to high harmonic pollution level, 183

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Fig. 8. The HPR values determined for the system with the investigated points.

For the worst considered harmonic levels, the maximum HPR value is 0.73 at P4 for the proposed approach, as compared to that of the traditional and no-filter cases. Besides, the difference between the HPR values for P2 and P3 validates that the nonlinearity of the load side is the dominant parameter in HC aggregation, when compared to the utility side's background voltage distortion. 5. Conclusions The maximum penetration level of the DG units or the system's HC is conventionally determined by regarding bus voltage rms limits and the current carrying capability of the supply lines. On the other hand, installations of PV-based DG units in the distribution systems have increased rapidly over the past decade. These DG units have inverter interfaces for connection to the grid, and these inverters inject harmonic pollution into the system. Consequently, a few recent studies considered the harmonic pollution issues in assessing the system's HC level. However, in these studies, only individual and total voltage harmonic distortion limits were taken into account as the harmonic constraints for HC assessment, because their systems consisted of only DG units as nonlinear equipment and did not have nonlinear loads, which introduce highly distorted currents. In this study, the maximum penetration level of PV-based DG units, hosted on a distorted distribution system having both background voltage harmonic distortion and nonlinear loads, was determined first as an optimization problem. The bus voltage limits, the current carrying capacities of lines, and the harmonic distortion limits were taken into consideration as the design constraints. In the optimization algorithm, the Newton-Raphson method was used to calculate the fundamental voltages and currents of the system, and harmonic power flow to find the non-fundamental harmonic voltages and currents. Using the developed algorithm, the HC level of the typical two-bus distribution network that supplies industrial nonlinear loads was investigated for various cases of utility side's background voltage harmonic distortion (UBVD) and load side's nonlinearity (Kn). The simulation-based test results show that both UBVD and Kn would limit the hosting capacity of the simulated system. Further, Kn is the dominant parameter in HC aggregation, as compared to UBVD. Second, a single-tuned passive harmonic filter was employed as a harmonic mitigation method to maximize the system's HC level. Therefore, the optimal single-tuned filter design algorithm was incorporated into the developed HC assessment algorithm. The genetic algorithm (GA) was used for solving the two nested optimization problems because of its computational efficiency and its convergence to the global solution in a short time with acceptable accuracy. Based on the results of the uncompensated system, as also those of the system compensated with a shunt capacitor, the proposed and the

Fig. 7. The impact of filter design on the system's HC level for all UBVD and Kn intervals: (a) conventional approach, (b) proposed approach.

and one indicates that either the system is sinusoidal or the harmonic pollution level is too low to affect the DG hosted in a manner similar to the concept of de-rating of electric equipment, such as cables and transformers under non-sinusoidal conditions. Therefore, this ratio clearly reflects the impact of harmonics on the system. To understand the effect of the designed filter on the HPR results, four points, P1, P2, P3 and P4, on the obtained HC surface, which represent the four corners of the surface shown in Fig. 7(b), are investigated. For the simulated test, P1 represents the sinusoidal system, i.e. Kn = 0 and UBVD = 0; P2 the point where the load side is the main harmonic source, i.e. Kn = 25 and UBVD = 0; P3 the point where the utility background voltage is the main harmonic source, i.e. Kn = 0 and UBVD = 4.5; and P4 the point with the worst considered case of harmonic distortion, where both load and utility side harmonic distortions exist, i.e. Kn = 25 and UBVD = 4.5. The value of the maximum allowable DG capacity, under sinusoidal conditions, is calculated as 7.5 MW. Consequently, the magnitudes of HPR for the four points of the proposed and conventional approaches are given in Fig. 8. From these values, it is evident that the proposed filter provides better HPR for P2, P3, and P4, and thus the effectiveness of the proposed approach is validated. At P1, the filter provides only reactive power into the system. 184

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traditional optimal single-tuned filter designs were comparatively evaluated to demonstrate the advantages of the proposed design in improving the system's HC under distorted voltage and current conditions. The results show that the proposed design contributes to considerably better improvement in HC, in comparison to the traditional approaches, particularly at high harmonic distortion ranges. A new definition of harmonic penetration ratio (HPR) was used to assess the impact of harmonics on the hosting capacity, where the maximum allowable HC under non-sinusoidal conditions can be calculated and compared to that of a case where the loads and the DG are harmonics-free. This ratio can accurately reflect the impact of harmonics on the system's HC. With time-varying loads or maximum generation conditions, using switched capacitors or static var compensators as well as energy storage technologies can overcome the overvoltage issues resulted from high DG penetration and light load conditions, and will enhance or at least maintain the system's HC at its adequate level. The findings of this point will be investigated in future works. Finally, power quality will play a significant role in the future smart grids to guarantee delivery of clean energy to customers with stricter limits and mechanisms for power quality tracking and identification using reliable communication networks.

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