A harmonic power market framework for compensation management of DER based active power filters in microgrids

Electrical Power and Energy Systems 113 (2019) 916–931

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

A harmonic power market framework for compensation management of DER based active power filters in microgrids

T

Abbas Marinia, Mohammad-Sadegh Ghazizadeha, , Seyed Saeedallah Mortazavib, Luigi Piegaric ⁎

a

Department of Electrical Engineering, Shahid Beheshti University, Abbaspour College, Tehran 1983969411, Iran Department of Electrical Engineering, Shahid Chamran University of Ahvaz, Ahvaz 6135783151, Iran c Department of Electronics, Information & Bio-Engineering, Politecnico di Milano, Milan 20133, Italy b

ARTICLE INFO

ABSTRACT

Keywords: Active power filter Distributed energy resources Harmonic power market Expected payment function Optimization Microgrids

Harmonic distortions are going to be more important in the near future due to widespread employing of power electronic based devices. The quality of power may get degraded without using proper mitigation methods. On the other hand, new paradigms of deregulated markets which make the power a competitive product as well as customer inclinations to pay for a high-quality power, inspire distribution companies to enhance the power quality level. Hence, various investigations should be considered to meet the power quality standards in electric networks. In this paper, a market-based framework is proposed for central management of harmonic compensation actions in microgrids (MGs). Since distributed energy resources (DERs) are prevalent in MGs, the compensations actions could be based on DERs activities in addition to conventional active power line conditioners (APLCs). Hence, a detailed investigation of harmonic filtering capabilities of various DERs is firstly represented. Afterward, a global model is proposed for various harmonic active power filters (APFs) either based on DERs or APLCs. To comply with the obligations of deregulated power markets, a new concept named as harmonic power market (HPM) is proposed for economic management of various APF resources participating in harmonic mitigation actions. Furthermore, a distortion power expexted payment function (DEPF) is introduced for each APF participating in the HPM. The HPM framework is modeled as an optimization model subject to various standards, technical and systematic constraints implemented in some case studies. Simulation results show the capability and performance of the proposed model for optimal management of various APF resources in harmonic compensation. Increasing in harmonic filtering capability, deferring the requirements for installation of new APLCs as well as a decrease in harmonic compensation costs are the main advantages of using DER based APFs in the HPM.

Nomenclature In this paper, single parameters, single variables, and matrices of variables and parameters are shown with capital letters, small letters, and capital letters in brackets, respectively. The notations used in the paper are as following: Abbreviations APF DFIG DER DEPF DS GSC

active power filter doubly fed induction generator distributed energy resource distortion power expected payment function distribution system grid side converter

LOC MG MSC PCC PE PQ THD VSWT Indices

loss of opportunity cost microgrid machine side converter point of common coupling power electronic power quality total harmonic distortion variable speed wind turbine

I F H

network buses set of available APF resources harmonic order

Corresponding author at: Shahid Beheshti University, Abbaspour College, East Vafadar Blvd., Tehranpars, P.O. Box: 16765-1719, Tehran, Iran. E-mail addresses: [email protected] (A. Marini), [email protected] (M.-S. Ghazizadeh), [email protected] (S.S. Mortazavi), [email protected] (L. Piegari). ⁎

https://doi.org/10.1016/j.ijepes.2019.06.020 Received 18 September 2018; Received in revised form 24 May 2019; Accepted 6 June 2019 Available online 20 June 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

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superscripts

processes. Residential and commercial appliances could inject remarkable harmonic levels into the network. It has been reported in [5] that the low voltage network of Europe is suffered from high levels of harmonic distortion generally due to harmonics of modern residential power electronic devices. In higher voltage levels this harmonic distortion is obviously reduced. Although residential loads are individually small, cumulatively they may inject high harmonic level to network. In addition to the small loads, large nonlinear loads in commercial and industrial appliances such as rectifiers and motor drives could also be as notable sources of harmonic pollutions [6]. Moreover, DERs are usually connected at distribution levels due to their power and voltage ranges [7]. Since power electronic interfaces are used as power conditioning units, DERs may insert some level of harmonics into distribution networks [8,9]. Therefore, DSs and MGs are usually suffering from more harmonic distortions compared to transmission levels. These harmonic distortions could affect PQ in the MG and also performance of the exsiting control methods such as droop control method [10]. In the grid-connected mode of the MG, properties of stiff grids such as voltage and frequency may not get affected excessively by harmonic disturbances. In this mode, the voltage profile of the network will be fluctuated in an acceptable range [11]. However, in islanded mode, harmonic distortions are more challengeable due to the inability of the slack bus to maintain voltage and frequency [9,12]. It could affect the stability of the local network and performance of the droop control method. Hence, MGs as an especial kind of DSs could be more susceptible to harmonic distortions. This may deteriorate PQ levels in MGs including PQ sensitive loads. Unlike the transmission level, harmonic sources are more dispersed in the MG. Moreover, harmonic sources might not be dominant and may inject harmonics at any point at any voltage level. Hence, the exact pre localizing of harmonic injections could be difficult. Therefore, it seems that following two important issues will be dominant in the future MGs:

Sync synchronous Stat stator Rtor rotor Notations A availability matrix of APFs in buses D (DI, DV, DH) distortion power (for current, voltage, and harmonic distortion powers, respectively) D1, D2 maximum available distortion power in two working regions of DEPF G gain factors of internal control blocks of the GSC I bus injection currents Nf total number of APFs Nh total number of harmonics P active power Q reactive power S apparent power Sl slip of induction generator V bus voltages w1, w2 binary variables respectively for working regions of 1 and 2 of DEPF Δ phase angle of voltage Θ phase angle of current π0, π1, π2, π3 bids of APFs for availability cost, cost of losses, adjustment of active power, and reactive power, respectively ρ0, ρ1, ρ2, ρ3 price of HPM for availability cost, cost of losses, adjustments of active power, and reactive power, respectively Ω angular frequency 1. Introduction Nowadays, a large part of loads in modern electrical distribution networks relies on power electronic (PE) interfaces due to their flexibility and controllability. They usually unveil a nonlinear behavior and insert some levels of harmonics into the network. The power quality (PQ) may get degraded due to these harmonic distortions. Hence, proper mitigation methods should be employed for enhancing power quality in electrical networks. On the other hand, modern devices used by consumers are more sensitive to power distortions. This makes them indigent to a high-quality input power and indicates the importance of mitigation of PQ related problems. Besides, from the power market point of view, customers are also going to be more concerned about the 'quality' of power they paid for. Deregulation in the power industry leads electric power to be a competitive product with specific properties. Clearly, the more power quality the more power welfare for customers. All of these considerations result in an increasing attempt for mitigation of harmonic distortions by distribution companies. Clearly, all market players will benefit from a high-quality level of electric power. Traditionally, passive filters, static compensators, and active power line conditioners (APLCs) have been employed to mitigate harmonics effects. Due to higher flexibility, there is an increasing approach in PEbased active harmonic filters such as APLCs. They could be the optimal choices to cope with the PQ related problems. In addition to the conventional APLCs, almost all energy resources with PE interfaces may be controlled to act as harmonic active filters [1–4]. Hence, these two groups of harmonic filters could generally be known as active power filters (APF). Harmonic distortions are challengeable in distribution systems (DSs), especially in microgrids (MGs). MG is a kind of DS consisting of local loads, distributed energy resources (DERs) as well as management systems which could operate in connected and off-grid modes. PE-based nonlinear loads as the primary sources of harmonic distortion are being utilized in various home and commercial appliances, and industrial

• The •

growing penetration of PE based loads imposes increasing harmonic currents to MGs. These loads are either uncontrollable or are out of control of the MG operator. The growing penetration of PE interfaces based DERs, provide an additional opportunity for mitigation of harmonics in MGs. The optimal coordination of these APF resources may be managed by the MG operator.

The main idea behind this paper is to propose a framework for the coordinated operation of DER based APFs and APLCs to mitigate harmonic distortions in the MGs. The coordination mechanism is achieved in this paper via a market-based framework named as harmonic power market (HPM). To develop a market framework, a new payment function concept named as distortion power expected payment function (DEPF) is proposed for each APF. In the HPM paradigm, each APF resource may submit its DEPF bids to the market operator. The market operator determines required harmonic injection currents of the APFs for satisfying harmonic standards throughout the network. The compensation reference currents are then transmitted to the APFs by available communication infrastructures of the MG. The centralized control of APFs guarantees optimal harmonic compensation with respect to the local controls. This may also avoid unwanted instabilities and interference caused by the un-coordinate operation of APF resources. 1.1. Related works Harmonic compensation methods by APFs could be categorized in single APF, parallel APFs and distributed APF schemes. Although there is a great body of literature about modifying control loops of individual DER based APFs to cope with PQ problems [13–15], fewer investigations are done for parallel APFs [12,16–19] or distributed APLCs 917

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[20–22]. Harmonic compensation by APLCs are addressed in numerous literature and the reader may find a good review of various configurations and control methods in [23]. Harmonic filtering using DER based APFs is almost a new concept. In [1,2] an APF based on a wind turbine power plant is employed which could simultaneously capture maximum wind power and improve PQ level of the MG. A harmonic compensation scheme is also proposed in [4] by a wind generator to inject harmonic compensation currents via its stator to the grid. A Harmonic compensation scheme using a PE interface of a photovoltaic power plant is reported in [14]. A review for harmonic compensation methods using DER converters is represented in [24]. Usually, control methods proposed for parallel APLCs and DER based APFs, try to develop or modify internal control loops of the individual DER units. In [12] a harmonic control droop is proposed for reducing harmonic distortion in the point of common coupling (PCC). A hybrid compensation technique is proposed in [16] using static VAR compensator and battery energy storage working in parallel. In [17] a hierarchical control structure is employed with two primary and secondary control levels. In the primary level, a droop controller is used to share harmonic powers. In the secondary level, a centralized controller manages harmonic compensation between parallel APLCs and DERs. However, single control of APFs could just be optimal for compensation of harmonics at installed bus and there is no guarantee for global optimality throughout the network. Distributed harmonic mitigation techniques provide better operation of APF resources. Distributed techniques in literature stand for APLCs located at different buses. A distributed active filter system is proposed in [21] for mitigating harmonic distortion in DSs. It consists of several distributed APLCs operating as virtual impedances. There are some modifications to this control method such as automatic adjustment of volt-ampere characteristic [22], and variable harmonic conductance [25]. A communication link is used in [20] to share the control signals between two distributed APFs. In [26] a control strategy for distributed DER is proposed based on a PQ index minimization. The state space is used to develop an optimization model to obtain reference currents of DER. The same authors, further develop the model to consider time delays in [27]. However, utilized matrices depend on DS parameters and the location of harmonic loads. To the author's knowledge, this paper is the first try to develop a market-based framework for the coordination of APF resources. The HPM establish a coordination mechanism for APFs to participate in harmonic mitigation activities. The HPM may have some similarities with the concept of the reactive power market. Reactive power providers submit their bids to the market based on reactive power expected payment function. Reactive power payment will be paid for availability cots, losses and loss of payments [28,29]. An expected payment function is proposed in [30] for modeling expected revenue of reactive power providers in the market. Some examples of operating wind turbines for reactive power support in the grid could be found in [31,32]. In [30] a multi-objective clearing mechanism is proposed for the reactive power market. Electric vehicles capability for reactive power support is also investigated in [33].

resources available in MGs is performed. Furthermore, a general model is proposed for harmonic modeling of APFs representing internal topology and control method of the APF. Accumulating all the above discussions, paper contributions could be summarized as follows:

• A detailed review for harmonic filtering capability of DERs is pro• • • •

vided based on primary energy resources and their energy converters. It includes all available possible APF resources in the MG based on APLCs and DERs. A general comprehensive model is proposed for modeling of APF resources. It could represent the effects of various control methods, internal topology, and conditions of primary energy resources. The proposed model could also be used in other harmonic or PQ studies employing DER based APFs. Harmonic working constraints of APF resources are proposed based on harmonic filtering capability and harmonic model of the APF. The proposed constraints may successfully determine the working regions of the filter. For market purposes, an expected payment function named as DEPF is proposed for each APF participating in the HPM. The market operator employs DEPFs of all APFs for economic calculation of compensation actions based on an optimization problem. Finally, the HPM concept is introduced, described and formulated for the management of harmonic mitigation activities of APFs in the MG.

The required compensation currents determined in HPM, are then transmitted to the APFs by available communication links. The harmonic compensation scheme does not get affected by the location of harmonic injections and APF resources. Note that harmonic content of network is an important input for the market optimization algorithm. APFs compensate harmonics continuously due to variable harmonic injections and operating condition of loads. Hence, it is proposed to use harmonic stats estimation for extraction of harmonic content in this paper. The rest of the paper is organized as follows; APF resources based on APLCs and DERs are introduced in Section 2 in Section 3, modeling of APFs in harmonic analysis and distortion power expected payment function are represented. The proposed HPM concept and related working constraints are proposed in Section 4. In Section 4, the HPM implementation is reported and finally, in Section 6, some discussions are provided. 2. Active power filter resources In this section, various available APF resources in the MG are introduced. APFs may generally be categorized as APLCs and DER based PE inverters. This section will be ended by introducing a general model for all APF resources of the MG. 2.1. Active power line conditioners APLCs are of the most important equipment used for harmonic compensation. They do not suffer from conventional limitations of passive filters and consequently are going to be more employed in electric networks [34–36]. An APLC is a voltage/current source inverter which is controlled to produce desired harmonic compensation currents at its output. The inverter injects a reversed (with 180 degrees phase difference) harmonic voltage/current to the network to eliminate the harmonics in the source side. Unlike passive filters, APLC produces no resonance in the network. Hence, they are more prevalent despite their higher investment cost and more complex control [34–36]. Schematics of shunt and series APLCs are represented in Fig. 1. Voltage and current signals are measured from the network and fed to the APF controller. The controller determines the required reference harmonic currents to be injected by the APF. There are various methods for producing

1.2. Paper contribution In this paper, an HPM is proposed for central management of harmonic compensation actions of APF resources in the MG. To this end, a DEFP is proposed for each APF representing various imposed costs for participating in the HPM. It consists of three main costs called availability cost, cost of losses and adjustment power cost. The market operator determines compensation actions of APFs via an optimization problem limited to various systematic and technical constraints. Some new harmonic constraints are proposed for each APF for modeling harmonic behavior based on its topology and functionality. In order to develop a complete compensation scheme, a detailed review of APF 918

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Fig. 3. Variable speed wind turbine.

employing these two energy converters may also participate in the HPM. However, synchronous generators have an inherent limitation to produce controllable harmonic currents in the stator. The common model of a synchronous generator in harmonic studies is an inductor in parallel with a resistor. They should be treated as a simple load and could not be accounted for an APF. In the following, both APF resources based on induction generators and PE inverters are introduced.

Fig. 1. Shunt Active Power Filter for a 3-phase 4-wire system.

reference currents of the inverters [26,37]. Anyway, the calculated reference currents are then fed to the grid by a proper switching method. The same principle is used for series APLC, except the fact that it should inject harmonic voltage to the network. Usually, the power is transferred to the network from a DC voltage link which is powered by an external source or even by a grid-connected DC converter.

2.2.1. Induction generators Induction generators are commonly used in wind turbines and micro-turbines. The rotation speed could vary in a broad range from lower speeds up to much higher speeds than synchronous speed. Induction generators are employed in various types of wind turbines. There are several common configurations for induction generators as; fixed speed wind turbines, variable speed wind turbines (VSWT) and doubly fed induction generators (DFIG). Fixed speed wind turbines use reactive power input for normal operation, i.e. they are reactive power consumers. Normally, capacitor banks are used to provide their reactive power requirements. However, this type of generators may not provide any harmonic compensation current. Neither stator nor capacitors could be controlled to inject harmonic compensation currents to the network. VSWT employs PE interfaces for direct connection to the network as shown in Fig. 3. Usually, two back-to-back AC/DC and DC/AC converters are used in the drive train. These two converters are known as machine side converter (MSC) and grid side converter (GSC), respectively. The existence of controllable full-sized GSC conveys a great capability of harmonic compensation for VSWTs. The power transferred from the wind turbine, charge a DC capacitor link between the MSC and the GSC. The GSC is a voltage source inverter which delivers the power of the DC voltage link to the grid. Hence, by proper control of the GSC, desirable harmonic injections could be extracted and VSWT could be accounted as an APF source. However, some small modifications in control loop or design parameters of PE converters are necessary. Working principles of VSWT

2.2. DER based active power filters DERs are becoming more prevalent in the power industry for various reasons such as reducing fossil fuels, low-cost natural energy resources and changing system paradigms from central to distributed generation. DERs include a broad variety of technologies such as wind turbines, photovoltaic systems, fuel cells, micro-turbines, and various energy storage systems. Due to their medium ratings and also geographical dispersion of primary energy resources, they are more connected in distribution levels in modern smart MGs [7,38,39]. DERs are connected to the network by three main energy converters; induction generators, synchronous generators, and static power converters. Electrical characteristics of DER are generally determined based on its energy converter. Energy converter imposes its characteristics on the output power of DER and it may secure DS from unwanted disturbances of primary energy resource. Some possible connections of primary energy resources and energy converters are presented in Fig. 2. DER Capability for harmonic compensation mainly depends on the type of energy converter and control strategy of the unit. Some types of energy converters like static power converters and induction generators have the ability to inject harmonic currents either by voltage source inverter or stator of the machine. It's possible to control a voltage source inverter (or current source inverter) to inject harmonic currents by controlling its reference current [17,24]. An induction generator may also inject harmonic currents from its stator [1,2]. Hence, DERs

Fig. 2. Different connection of DGs and energy converters. 919

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Fig. 4. Doubly fed induction generator.

Fig. 5. Harmonic model of DFIG in stator control mode.

for harmonic compensation are the same as in APLCs. Hence, the harmonic model of VSWT as an APF is the same as other PE based inverters and will be introduced in the next subsection. DFIG shown in Fig. 4 has a great capability to operate in a broad range of wind speeds. The stator is directly connected to the network and the rotor is connected to the grid via MSC/GSC converter pairs. The MSC is responsible for controlling voltage and current of the rotor circuit. The voltage of the DC link is adjusted by the GSC. Despite VSWTs in which energy converters deliver the total power to the grid, in DFIGs the rotor circuit just delivers a small fraction of total power. The active power in the rotor circuit is directly proportional to the working slip of the machine as shown in (1a). The positive sign in (1a) is for subsynchronous mode. Maximum capacity of the GSC is usually assumed to be about 25–30% of rating power of induction generator as shown in (1b).

controlled with reference power, quadratic current of the rotor is controlled with reference reactive power, and finally, the harmonic reference current is controlled by the nonlinear current of the load. The reader could find some details about control methods of DFIG using direct-quadratic theory in [1–4,40]. The harmonic model of DFIG in the stator control mode is shown in Fig. 5. The magnetizing branch is removed from the equivalent circuit of induction generator. Harmonic slip is defined as (2a) in each harmonic order and rotor parameters are in the stator side. The harmonic dependent impedance of DFIG in stator control mode could be modeled as (2b). To determine harmonic injection currents of the DFIG, Norton equivalent of Fig. 5 would be more convenient. Norton current could be determined as (2c). Complete harmonic model of the DFIG in the stator control mode will be represented in introducing the general model of APFs.

(1a)

P rtor = ±sl·P stat

S GSC

(25%

30%) SDFIG

slfh =

(1b)

Both MSC and GSC of DFIG could be controlled to deliver harmonic power from stator or rotor to the grid, respectively. Hence, two different harmonic compensation modes could be introduced as:

rtor f

sync rtor f

DFIG Zfh = Rfstat +

• Stator control mode: in this control method, harmonic compensation •

h

rotr i fh =

currents are injected to the network via stator. By a proper control method, MSC controls the voltage and current of the rotor circuit to deliver harmonic power in stator based on the induction mechanism. This approach has been employed in [1–3]. GSC control mode: in this control mode, harmonic compensation is provided by the GSC. The GSC based on available non-active capability and desirable reference current injects harmonic power to the grid. In this control mode, harmonic compensation currents do not flow in the stator circuit. This approach has been employed in [4,40].

rotr vfh DFIG sl·Zfh

(2a)

Rfrtor s

+j

stat fh (Lf

+ Lfrtor )

(2b)

(2c)

2.2.2. PE interfaces A large part of APF resources relies on PE interfaces of DERs. They have the same compensation principle as APLCs, and typically act as a shunt APF injecting compensation currents at the network. The PE interfaces basically used for power conditioning purposes, but it could also be controlled to deliver harmonic compensation power [14,24]. A comprehensive review of various topologies of PE inverters employed for PQ improvement is reported in [41]. General configuration of some DERs using it couldb PE interfaces, is shown in Fig. 6. A be seen, various primary energy sources deliver power to the DC voltage link. Then, the GSC injects harmonic power from the DC link to the MG as a voltage source inverter. Some possible primary energy resources available to serve as APF are as following:

Theoretically, harmonic compensation capability in stator control mode could reach to nominal capacity. However, some limitations might be imposed in practice due to the effects of harmonics on machine windings. Moreover, injecting harmonic currents by the stator (which basically has not been designed to produce harmonic currents), may degrade lifetime and performance of the DFIG. On the contrary, harmonic compensation currents produced in the GSC control mode, do not flow in machine windings. The harmonic capability depends on working slip and capacity of the GSC and is about 25% of nominal capacity. Working principles of DFIG controlled in the GSC control mode have many similarities with PE based APFs and will be discussed in the next subsection in more details. In the stator control mode, the MSC controls the voltage and current in the rotor circuit. Reference active power is calculated using maximum power point tracking algorithm from wind speed to capture maximum power. Reference reactive power is determined based on grid codes and network requirements. Grid codes dictate the continuous operation of the DFIG at a specific power factor and in a voltage and frequency range [31,32]. Control of active, reactive and distortion power may be performed simultaneously with various methods in the control loop. For example in [1,2], the direct current of the rotor is

• VSWT and fixed speed types which employ PE interface and DFIG controlled in GSC control mode. • Photovoltaic generators which deliver DC output power. • Various types of Energy storage systems such as batteries, supercapacitors, flywheels and so on. • Fuel-cells which use hydrogen fuel to produce electricity and water. • Micro-turbines produce a high-frequency output voltage. Electric equivalent circuit of the GSC could be found in literature as a voltage source inverter [42–44]. Equivalent impedance could be calculated in sequence, direct-quadratic and phasor domain. The general configuration of PE based APFs is similar to the model of Fig. 5. The voltage of the rotor is replaced by DC link voltage and Zf represents internal impedance of GSC converter. A simple model for the impedance of GSC could be determined in (3) [42,43]. The gain factor of GSC in (3) represents a group of gains for various internal control 920

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Fig. 6. Configuration of PE based active power filters.

blocks of the device. Similar to the stator mode DFIG control, the model for PE based APFs could be transformed into the Norton equivalent model. Some other devices such as static VAR compensators, STATCOM, and FACTS devices could also be accounted for APFs [45]. GSC Z fh = RfGSC + j

GSC fh Lf

GfGSC

Table 1 Various APFs modeled by the proposed model.

(3)

Type

APF

'int'

Zfh

Xf

I II III

DFIG (stator mode) PE based inverter APLC

'dfig' 'gsc' 'aplc'

(2b) (3) (3)

Trans Trans + filter Trans + filter

3. APF participation in the harmonic power market

2.3. The general model of active power filters

APF resources inject harmonic compensation currents to the MG. Hence, a fair payment should be made for provided distortion power correction service. In this section, the DEPF for APFs and related working constraints are introduced. APFs bid for distortion power correction to the MG operator based on their DEPF. However, at first, it is necessary to give a unique definition for distortion power.

In this section, a general model is proposed for various APF resources covering all aspects of APFs. The proposed APF model developed based on the Norton equivalent model is shown in Fig. 7. Internal current injection of APF is shown with a controlled current source. It is controlled by internal variables of DER controller such as the voltage of DC link, voltage, and current of MSC in rotor circuit of DFIG and some other variables like wind speed, radiation of the Sun, ambient air temperature and so on. However, controlled variables are not handled by the MG operator. The MG operator just determines the required harmonic injection. APF should control the current source with respect to the internal parameters to cope with MG operator's orders. The model in Fig. 7 is validated for all APFs and the required modifications are represented in Table 1 for each APF type. APF Type I is based on DFIG controlled in stator control mode. Hence, internal current, internal voltage, and output current stand for injection current of the rotor, output voltage of the stator, and current of the stator, respectively. Internal impedance is introduced in (2b) and connecting reactance is just for modeling of the transformer. APF type II is for PE based inverters which inject harmonic compensation currents from GSC to the MG. Hence, the internal current stands for current driving from DC voltage link. Moreover, current and voltage stand for current and voltage of GSC, respectively. Internal impedance was previously formulated in (3) and X, represents the reactance of output filter and transformer. APF of type III is for APLC and has the same working principle with type II. An important characteristic of type III is that all APF capacity could be used for injecting distortion correction power. Hence, there is no consideration for power transactions in fundamental frequency. Furthermore, type III APFs could not work in LOC region and all available capacity could be used for its harmonic compensation. The proposed model will be used in the next section to develop working constraints on APFs.

3.1. Distortion power In harmonic studies, harmonic voltages and currents are superimposed to the fundamental voltage and current. Hence, for a device working in harmonic condition, voltage and current should be replaced with their harmonic root mean square equivalents as shown in (4). Nh

v 2 = v12 +

vh2

(4a)

h=2 Nh

i 2 = i12 +

ih2

(4b)

h=2

The definitions for active and reactive powers is somewhat different in harmonic conditions. By the definition, active power is the average of instantaneous power and could be calculated as (5a). It contains fundamental and harmonic active powers. Despite active power which has a unique definition, there is no generally accepted definition for the reactive power in the presence of harmonics. Reactive power is defined at the complete sinusoidal condition and in the non-sinusoidal situation, no definition includes all properties of reactive power [46]. Definition of IEEE standard 1459 is adopted in this paper for reactive power [47]. By this definition, reactive power is just defined for the fundamental frequency as shown in (5b). It is also possible to define a harmonic reactive power for harmonic components as (5c) similar to the harmonic active power in (5a). However, harmonic reactive power is just a definition and does not contribute to the total reactive power. Nh

P = p1 +

Nh

ph = v1 i1 cos( h=2

1)

+

vh ih cos( h=2

Q = q1 = v1 i1 sin(

qh = vh ih sin(

1

h

1)

1

h)

h

h)

(5a) (5b) (5c)

All power transactions except fundamental active and reactive powers could be known as distortion power. To formulate the distortion power, apparent power in harmonic condition should be firstly calculated by

Fig. 7. The proposed general model for APFs. 921

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the product of root mean square values of voltages and currents as shown in (6a). Accordingly, distortion power would be determined as the difference between apparent power and fundamental apparent power as shown in (6b). Note that, harmonic active and reactive powers, are included in the third term of the distortion power. The first, second and third terms of distortion power in (6b) are known as current distortion power (DI), voltage distortion power (DV), and harmonic distortion power (DH), respectively.

S = vi =

v12 +

Nh

vh2 i12 +

h=2

d2 = S 2

v12 i12 = v12

Nh

ih2 + i12

h=2

Nh h=2

i fh =

(6a)

vh2 +

Nh h, k = 2

vh2 ik2

(6b)

=

int vfh

Xfh

sin(

int vfh v fh

Xfh

fh )

sin(

j int (v fh cos( Xfh fh )

+j

fh )

int vfh v fh

Xfh

vfh)

cos(

fh )

(7a)

(vfh ) 2 Xfh

int 2 2 (v fh )

Xfh

=

int 2 vfh vfh

Xfh

(7c)

• Primary-energy

source constraint: available mechanical/electrical power of primary energy source imposes another constraint on the APF. In harmonic condition, active power is the summation of all harmonic active powers. The calculated active power of the APF should be in the range of output power of the primary energy source. This constraint will be modeled in Section 4 in the HPM model (constraint (14e)).

Finally, constraints for DER based APFs are; available mechanical power of primary energy source, current limit, and voltage limit for various internal equipment, maximum volt-ampere capacity and harmonic power transaction capability of the APF.

• Voltage limit constraint: due to the insulation condition of the APF,

•

jXfh

2 P fh + Qfh +

The distortion power capability of APFs directly corresponds to the available harmonic volt-ampere capacity. Some functional and practical constraints are imposed on the APFs participation in the HPM. In this subsection, practical constraints which should be concerned for distortion power capability curves are introduced. The imposed constraints with respect to the APF model in Fig. 7 could be described as the following:

•

vfh 0

fh

Sfh = Pfh + jQfh = vfh i fh =

3.2. APF modeling in the HPM

•

int v fh

(7b)

ih2

h=2 Nh

counterpart of conventional power transmission constraint of DERs [31,32].

the maximum available voltage of the APF is limited. Practically, this may impose a limitation on the APF. The model of this constraint will be represented in the HMP model in Section 4 (constraint (14a)). Current limit constraint: this may be due to the thermal limits of conductors carrying output currents of the APF. This constraint is usually due to the limitation of the interface inductor in the APF model. The current limit constraint will be modeled in introducing the HPM model in Section 4 (constraint (14b)). Volt-Ampere constraint: maximum available volt-ampere generation should be limited to the maximum capacity of the APF. In harmonic condition, all harmonic voltages and currents are contributed to the calculation of volt-ampere generation. Hence, all harmonic frequencies should be considered in this constraint which makes it a nonlinear linking constraint. The volt-ampere constraint will be represented in constraint (14c) in Section 4 in introducing the HPM model. Harmonic power transmission constraint: in all harmonic frequencies, the exchangeable harmonic power from APF is limited due to the constraint of the interface inductance of the model in Fig. 7. Phasor diagram of voltages and currents of the APF are shown in Fig. 8. Based on this model, harmonic current of the APF could be calculated as (7a). Harmonic apparent power will then be determined using voltage and current of the APF as shown in (7b). Due to harmonic active and reactive powers, an extra constraint will be imposed on the APF for limiting harmonic power transmission from APF to the grid. This constraint is mathematically shown in (7c). The constraint of (7c) could be accounted as the harmonic

3.3. Distortion power expected payment function Distortion power of APF resources should be calculated for payment purposes in the HPM framework. An expected payment function named as distortion power expected payment function, DEPF, is proposed in this paper for each APF participating in the HPM. The DEPF is based on the capability of the APF for injection of the distortion power correction. The capability of available distortion power correction capacity may be determined after calculation of the power transactions in the fundamental frequency. Clearly, distortion power correction injection increases the losses of the APF. If the APF is required to deliver more distortion power, then it may reduce its main power transactions considering the loss of payments. The proposed DEPF for each APF is shown in Fig. 9. The DEPF consist of two different working regions. Three main cost terms are shown in Fig. 9 as availability cost, cost of losses and loss of opportunity cost (LOC). Availability cost and cost of losses are imposed in region 1, but, costs due to adjustment of active and reactive powers are only imposed in LOC region. Availability cost is a fixed cost term for preparation in the HPM. Some amount of APF capacity should be unloaded and APF should be ready to inject distortion power by the operator's request. Capability to inject distortion power may impose various costs on the device and exact determination of all imposed costs may be difficult to calculate [29–31,33]. Availability cost is a fraction of total investment cost imposed for capacitating APF to inject distortion correction power. Some modification of the controller unit, cost of sensor and computer, and

Fig. 8. Phasor diagram of harmonic voltages and current of the APF.

Fig. 9. Proposed distortion power expected payment function. 922

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switch replacement are some remarkable costs to enable a unit for harmonic correction injection. It should be calculated based on the daily and hourly operation. Some typical values are specified in [29–31,33]. Anyway, availability cost is a fixed payment for covering this type of total costs. Distortion power increases losses in APF due to increase in output volt-ampere. The losses are generally for losses of switching and conduction of PE devices or effects of harmonic currents such as extra heat in machine windings. Hence, a payment is required for covering the cost of extra losses imposed to the APFs. Various approaches have been proposed for modeling of losses in literature for reactive power support of the DERs. In [29–31,33] a quadratic function is proposed for modeling of losses with respect to the output power of a PE inverter. Hence, the increase in APF losses could be modeled as a quadratic function of distortion power as shown in Fig. 9 in both regions. The cost of losses is imposed in both regions. The difference is that the required distortion correction power is more than the available un-loaded capacity of the APF in region 2. The maximum amount of increase in distortion power in region 1 without affecting fundamental power transactions could be determined as (8). Due to the low concavity of curve in region 1, some authors proposed using linear cost function for modeling of losses in this region [28,30–32].

(D1max )2 = (S fmax ) 2 f

Vf2,1 I f2,1

Pf ,1

Pf ,1

Qf ,1

Qf ,1

pf qf

max 2 2 (D2max ) f ) = (S f

(9a)

(Pf ,1

pf )2

(Qf ,1

qf )2

(9b)

Power adjustments should be modeled as free variables. It means that both increase and decrease in active and reactive powers are possible to increase distortion correction power capability. Some possible situations could be mentioned as follows:

• An APF injecting active power to the MG could decrease active power injection (Δp > 0). • An APF absorbing active power from the MG (charging mode) should increase its active power (Δp < 0). • An APF absorbing reactive power from the MG should increase reactive power injection (Δq < 0). • An APF injecting reactive power to the MG should decrease reactive power injection (Δp > 0).

The DEPF for each APF could be modeled as (10). The prices of π0, π1, π2, and π3 are the offer prices of the APF for availability cost in $/hour, cost of losses in $/MVARH, cost of active power adjustment in $/MW and cost of reactive power adjustment in $/MVAR, respectively. Offer prices of APFs for each cost term are multiplied to the corresponding power in (10) to constitute the DEPF. Adjustment active and reactive powers are modeled as quadratic functions. Absolute functions could also be used for adjustment power [32]. The proposed DEPF includes all various costs imposed on an APF for injecting distortion power in the HPM. Note that proper binary variables are also required for completely modeling of the APF working in both regions which will be introduced in the next section. The DEPFs of all APFs will be used by the MG operator to determine APF injection currents in the HPM framework.

(8)

It should be noted that despite reactive power, distortion power is not essential for the proper working of the APF and hence, payments for the cost of losses should be paid for any amount of distortion correction power injections. This is somewhat different from the payment functions proposed for DERs participating in the reactive power market [28–33]. Each reactive power provider may itself use some reactive power. This reactive power may be used either as internal requirements or network obligations by the grid codes. Hence, payments for the cost of losses for reactive power providers should be paid above the value of mandatory reactive power [30]. But, the distortion power is not of the unit requirements or grid codes (at least by now!), and payments should be considered for an amount of distortion correction power injection as shown in Fig. 9. In region 2, LOC payment should be added to the DEPF in addition to the availability cost and the cost of losses. In this region, requested distortion correction power by the MG operator is more than the available un-loaded capacity of the APF. Hence, the APF should reduce the active/reactive power transaction to release some amount of capacity for distortion correction power injection. A LOC payment should be considered due to loss of revenue in active and reactive markets. Despite the reactive power market which just active power could be modified for more reactive power capability; in the HPM, both active and reactive power could be adjusted. Hence, the following approaches could be implemented for an APF working in LOC region:

DEFPf = 0f + 1f d f2 + 2f pf2 + 3f qf2

(10)

4. Harmonic power market, concept and formulation APF resources are physically distributed in MG. Sizing of APLCs is determined using optimization models [34,35]. Likewise, DERs are placed in the MG according to available primary energy resources. In this section, the concept of HPM as a framework for the coordination of harmonic compensation activities is developed and formulated. 4.1. Harmonic power market concept For a reliable compensation scheme, control of distributed APF resources should be managed centrally by the MG operator. This could lead to a flexible optimal distributed compensation scheme. In this paper, it is proposed that a market-based framework to be employed for the coordination mechanism of APFs in MG. This market is named as harmonic power market (HPM). Some requirements and necessities to develop such a market could be outlined as follows:

• Release active power capacity • Release reactive power capacity • Release both active and reactive power capacity

• MGs should employ mitigation methods to cope with harmonic

In the first approach, the MG operator may obligate the APF to reduce its active power. Accordingly, active power mismatches should be compensated by other generation units. In the second approach, the reactive power capability of the APF is reduced to release distortion power correction capability. However, due to network voltage security constraints, this approach should be treated carefully. In the third approach, both active and reactive powers could be modified simultaneously. Power adjustments for fundamental frequency could be done in a way to keep working power factor of DER constant. By modifying the active and reactive power as (9a), the maximum distortion correction power capacity could be calculated as (9b) in region 2.

• 923

distortions imposed by increasing PE based loads and devices. Even when limits are met by the customers according to the standards [48], harmonic levels may sometimes be violated [49]. Furthermore, a large part of loads may impose an uncontrolled level of harmonics into the network. Note that harmonics could be amplified in resonance condition. Hence, proper filtering methods are required to meet the desired level of harmonics in the system. Harmonic filtering schemes based on APLCs (owned by the MG) may involve some challenges such as limited filtering capacity, fixed location of harmonic current injections and considerations related to their cost and expensive supplied compensation current. Employing

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•

DERs based AFPs could bring more filtering capability to the MG and requirements for installing new APLCs could be deferred. DERs are also dispersed in the network and could inject harmonic compensation currents across the network. Finally, it should be pointed out that harmonic filtering capability could be employed as a side service from DER based APFs. It could decrease some cost terms if harmonic compensation currents get supplied from these APF resources. The costs may just include some modifications to control methods of DERs as outlined in Section 3. Since DERs could be owned by other parties rather than MG operator, a fair competition framework should be created for managing the participation of various APF owners in the harmonic compensation. Power markets for energy and some ancillary services such as regulation and reactive power are prevalent [50] and their structure could be employed for establishing a similar market for managing harmonic powers. Hence, an HPM may be employed for the participation of various APF owners in harmonic compensation activities in the MGs.

•

•

Hence, the HPM is established for the coordination of harmonic compensation activities of various APF resources. The proposed framework is shown in Fig. 10. In the proposed HPM, the MG operator is responsible to receive distortion correction power bids from APF owners as well as their working constraints. The MG operator will determine the required compensation distortion correction powers of APFs to meet the desired level of harmonics. The HPM is modeled as an optimization problem with the goal of minimizing payments to the distortion correction power providers subject to various constraints. Constraints and loading of network lines imported from distribution line owners, data of DER participation in energy and ancillary service markets and harmonic standards are of main constraints. Furthermore, network harmonic condition imported from measurement system is required to determine the level of required harmonic compensation. After running HPM, the MG operator sends calculated reference currents to distortion power providers. The APFs are responsible to adjust their outputs to comply with the MG operator orders. There are some considerations for the proposed HPM in Fig. 10 which could be summarized as follows:

Anyway, the proposed HPM is the first try to establish a market framework for managing harmonic mitigation activities of APF resources in the MG. APLCS and DERs owners are participants in the HPM and the MG operator pays for the provided distortion correction power. The harmonic levels would meet the desired standards and customer could benefit from a qualified power. Nevertheless, practical considerations and market aspects of the proposed HPM should be more investigated in future works. 4.2. Harmonic power market modeling The proposed HPM is modeled as an optimization problem subjected to constraints of APFs, constraints of harmonic standards and constraint of the network and market. It is developed based on concepts of optimal power flow and APLC planning. The complete model is represented in (11)–(15). The output of the optimization model is the reference compensation currents of the APFs required for the desired level of harmonic in the MG. The HPM model is described in the following. The objective function is defined in (11) based on minimization of the total cost of supplying distortion correction power from APF resources. Availability payment for all participant APFs in the HPM, cost of losses for APFs injecting distortion power, and payments for losses of revenues for APFs entering LOC region, have been considered in the (11). Various terms of provided distortion correction power should be multiplied by market prices for each term. The market prices are determined based on bids of accepted APF as shown in (12).

• The proposed HPM should be categorized in a proper accepted

•

the effects of power quality issues such as harmonic distortions, voltage flickers, voltage sags, and swells and also unbalances could be accounted for as quality services. It seems that quality services may play important roles in future electrical grids. Deregulated markets paradigms in both wholesale and retail markets, retailers' approach for delivering a high-quality power and customer desire to pay for a more qualified electric power could be accounted as of some reasons that may highlight the importance of the quality services. Besides, as the electric power industry moves toward the full competition, various services are being unbundled. Among them, third parties could participate to improve the quality of power in quality services. The HPM could be adjusted as a real-time market to mitigate harmonic related problems in the current operation status of the network. Furthermore, the market is implemented as sequential auctions in which the results of energy and ancillary markets would represent the starting point for the HPM market. The MG operator plays an important role in the reliable procurement of quality services while energy and ancillary services are being securely supplied.

market framework. The ancillary service market is a candidate which could be used for classifying the HPM. Ancillary services are denoted as those services other than the energy which are crucial for ensuring the reliable operation of the network. Various reserve powers, voltage control, and reactive power are of such ancillary services. However, desired harmonic standards may not be accounted for a necessity for the secure operation of the system. Hence, this classification could be challengeable. Besides the ancillary service market, the proposed HPM could be categorized as a quality service. The quality services could be defined as those services which are employed for enhancing the quality of the supplied electric power. Hence, activities to mitigate

Objective function: Nf

min

Nf

DEPFf = f =1

0

+

f =1

2 1 df

+

2

pf2 +

3

qf2

(11)

Constraints of (12) are proposed for modeling settlement method of the HPM which is considered to be as a pool market model. Prices of the market for all various terms should be higher than prices of all accepted APFs. Payments to the APF owners will be considered based on prices in the HPM, ρ1, ρ1, and ρ3. Active and reactive powers are exchanged in the spot power market and hence adjustment prices of ρ2 and ρ3 should be consistent with prices of energy in the spot power market [31]. Settlement of market:

1f w1f

Fig. 10. Proposed harmonic power market framework. 924

1

f

(12a)

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2 f w 2f 3f w 2f

2

f

(12b)

3

f

(12c)

Vf2,1 I f2,1

max 2 2 (D2max ) f ) = (S f

(Pf ,1

(Qf ,1

qf )2

(13d)

Qfmax = tg( f ) P fmax

(13e)

df2

0

2 w1f (D1max )2 + w 2f (D2max f f )

Nh

df2 = V f2,1

ih2 + I f2,1

h=2

Nh

vh2 +

h=2

Nh h, k = 2

vh2 ik2

(13h)

qf

qfmax w2f

(13i)

h=2

2 vfh

(V fmax ) 2

2 i fh

(S fmax )2

2

2 vfh

hXf

f,

hXf

Pf ,1 +

P fmax

pfh

(14c)

2

int v fh vfh

h

f

vih2

|Vi,1 |2 (THDimax ) 2

i

(14d)

(14e)

(15a)

vih2

|Vi,1 |2 (IHDimax ) 2

i,

(15b)

h

Nf

iih =

ifh

i,

h, Aif

0

(15c)

f =1

vih = vfh (Vimin ) 2

i, Nh

vih2

h, Aif

(15d)

0

(Vimax ) 2

i

i=1

Harmonic power flow constraints.

f

f

h=2

h= 2

APF modeling: Nh

Nh

Network modeling and Harmonic standards: Nh

The set of constraints of (14) have been proposed for modeling related constraints of the APFs. Harmonic voltages and currents of the APF, are limited to its rating values as shown in (14a) and (14b) respectively. The constraint of (14c) is used to limit the volt-ampere generation of the APF less than its maximum capacity. All harmonic voltages and currents should be considered for calculation of current loading of the APF. Maximum limit of harmonic powers transmission is modeled in (14d). Unlike the (14c), the constraint of (14d) should be considered in each harmonic order. The constraint of (14e) is proposed for limiting active power variations considering harmonic active powers. The available active power is directly proportional to the available mechanical/electrical power of the primary energy source of the APF.

V f2,1 +

(14b)

The set of constraints in (15) are proposed for modeling harmonic standards and network related constraints. Two first constraints are proposed for considering harmonic desired levels of total harmonic distortion (THD) and individual harmonic distortion (IHD) are given in (15a) and (15b) respectively. Typical levels of harmonic standards are 5% and 3% for THD and IHD, respectively [51]. The important goal of the HPM framework is the economic satisfaction of harmonic desired levels in the whole of the MG. Constraints of (15c) and (15d) are used for calculation of harmonic currents and voltages of network buses based on harmonic voltages and currents of the APFs. Matrix A is an availability matrix proposed for representing installation of fth APF at bus i, if and only if the element of Aif equals to one. In (15c), APF injection for each bus is determined based on the summation of compensation currents of all connected APFs. Also, the voltage of bus i should be equal to the voltages of all parallel APFs connected to the bus, which is modeled in (15c). Bus voltages should not violate the allowable ranges of maximum and minimum voltages as shown in (15e). Finally, the general constraint of (15f) represents a group of constraint which should be used for calculation of harmonic power flow in the MG. Frequency scan method is the common method for harmonic power flow. In this method, harmonic analysis is performed individually for each harmonic order after calculations of power flow in fundamental frequency [52]. Harmonic injections of nonlinear loads are determined based on the harmonic spectrum of load which is derived based on experimental tests. In this paper, harmonic power flow constraints are considered using a graph-based power flow method proposed by the authors in [7,52]. In this method, some topology-based matrices are developed for modeling of the network for fundamental and harmonic frequencies. The results of the power flow for fundamental frequency is used to calculate harmonic injections of nonlinear loads based on their harmonic spectrum [7,52]. Finally, the harmonic voltages and currents of the network will be determined using the power flow equations of the graph-based method.

(13g)

pfmax w2f

f

h=2

(13f)

pf

I f2,1 +

Nh

P fmin

(13c)

P fmax = 0.1Pf ,1

2 vfh

2 pfh + qfh +

(13b)

pf )2

(I fmax ) 2

h=2

(13a)

(D1max )2 = (S fmax ) 2 f

Nh

V f2,1 +

DEPF modeling:

1

2 i fh

h=2

The constraints of (13) are proposed for DEPF modeling for each APF. The working region is determined based on binary variables of w1 and w2 in (13a) for working in loss and LOC regions, respectively. Setting each variable to unity shows the corresponding working region of the APF. If two variables are adjusted to the zero, then just availability payments will be paid to the APF. Constraints of (13b) and (13c) represent limits of distortion power in two regions of DEPF. In region 1, the maximum available distortion power is determined based on its rating and current working point of the APF (13b). Maximum available distortion power of the LOC region is limited to allowable variation in active and reactive power adjustments. Maximum allowable variation in active power is set to 10% of the current working point as shown in (13d). Moreover, maximum reactive power variation is determined based on the fixed working power factor of the APF as shown in (13e). The constraint of (13f) limits distortion correction power injection of the APF to the maximum values in the corresponding working region. Calculation of the injection distortion correction power with respect to the harmonic voltages and currents of the APFs is modeled in (13g). Current distortion power, voltage distortion power, and harmonic distortion power are various terms shown in (13g). Finally, constraints of (13h) and (13i), are proposed for modeling maximum variation of adjustment active and reactive powers based on their maximum available values. Since adjustment powers are only allowed in the LOC region, then the binary variable of w2 has been used to limit their maximum variation in these two constraints.

w1f + w2f

Nh

I f2,1 +

(15e) (15f)

The harmonic content of the MG is an important input of the HPM. In real-time operation, the harmonic content is changing continuously since operational conditions and combinations of nonlinear loads are

(14a) 925

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Fig. 11. Modified IEEE 33 bus test network.

changing continuously. Hence, in real-time monitoring of system harmonics, it's necessary to update the harmonic content continuously. Various identification methods may be applied, but, since the harmonic sources may not be dominant and their location and type may be varied by time, it's proposed to use harmonic state estimation (HSE) algorithm. HSE is an efficient economic tool for identification of harmonic sources in electrical networks. In specific intervals, HSE updates harmonic content of MG. Then, the compensation actions of APFs may be recalculated by the market operator repeatedly. Finally, new reference currents will be updated and sent to the APFs at each time interval. It should be noted that if the communication link gets corrupted by any reason, the APFs controllers will be switched to the local control mode. The compensation may be done locally using droop control method or any other coordination algorithm [18]. This scheme enhances the reliability of the HPM. The local control mode could be available with some extra settings in the internal controller of APF. Operation in this mode will be continued until the re-connection of the communication link.

Table 3 Harmonic spectrum of nonlinear loads.

A modified version of the IEEE 33-bus test network is used to demonstrate the performance of the HPM framework. The network consists of 32 branches and 5 tie-switches as shown in Fig. 11. Line and bus data could be found in [52]. Four nonlinear loads were connected to the network and their active and reactive powers are represented in Table 2. A general non-linear load as a six-pulse diode bridge rectifier was adopted for all nonlinear loads. Harmonic spectrum of nonlinear Table 2 Characteristics of harmonic loads. Bus

P (pu)

Q (pu)

1 2 3 4

14 20 23 30

0.150 0.125 0.110 0.145

0.120 0.105 0.100 0.125

Magnitude

Phase

5 7 11 13 17 19

0.35 0.43 0.05 0.08 0.04 0.04

180 180 0 0 180 180

loads is used from [53] and is represented in Table 3. Harmonic spectrum approach is used for harmonic analysis [52,53]. In this approach, magnitude and phase of harmonic injections of nonlinear loads are used to calculate the flow of harmonic power in the network in each harmonic frequency. Locations of harmonic sources were assumed to be known in this paper. In a real situation, location and spectrum of nonlinear injections could be determined based on an harmonic state estimation algorithm. Four DERs were added to the network in selected buses as shown in Table 4. A parking lot including electric vehicles is considered at bus #12; a photovoltaic generator is installed at bus #21; a fuel cell system is connected at bus #24, and finally, a wind turbine employing DFIG is installed at bus #26. In order to simulate a real situation, a power flow program [7] was used to determine the flow of power. Active and reactive powers of DERs are also represented in Table 4. For harmonic analysis, a harmonic power flow algorithm [52] is used to determine the harmonic level of the network. THD of bus voltages considering DERs is shown in Fig. 12. As it is obvious, the THD standard is violated and it is above the standard level of 5%. Hence, MG operator should use available APF resources for harmonic compensation. To achieve the desired harmonic standard, some simulation cases will be provided. Data of all available APF resources in the MG are collected in Table 4. There are two APLCs and four DER based APFs. APLCs are based on a voltage source inverter installed at buses #3 and #10 as shown in Fig. 11. The internal impedances of APLCs were calculated by the method of [44]. The APLCs were installed by the MG operator for harmonic compensation without considering possible participation of

5. HPM implementation

Nonlinear load

Harmonic

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Table 4 APF resources of the MG. APF

Type

bus

Smax (pu)

Imax (pu)

Vmax (pu)

P1 (pu)

Q1 (pu)

D1max (pu)

V1 (pu)

π0 ($/h)

π1 ($/kVARH/h)

π2 ($/kW/h)

π3 ($/kVAR/h)

1 2 3 4 5 6

APLC APLC Electric vehicle Photovoltaic Fuel cell DFIG

2 9 12 21 24 26

0.32 0.26 0.02 0.03 0.02 0.16

0.43 0.35 0.1 0.15 0.1 0.25

1.1 1.1 1.1 1.1 1.1 1.1

0 0 0.013 0.021 0.013 0.091

0 0 0.007 0.009 0.005 0.042

0.32 0.26 0.013 0.020 0.014 0.125

0.989 0.942 0.931 0.991 0.985 0.961

17.4 18.8 4.6 7.2 5.6 9

860 900 430 395 420 380

2025 1620 1755 1575 2025 1620

1665 1413 1476 1395 1665 1413

the form of MINLP) was modeled in GAMS software using DICOPT solver [54] in a personal computer equipped with a 2.93 GHz Intel processor and 4 GB memory. Without loss of generality, it is assumed that the MG is working in grid-connected mode. Hence, the voltage at the PCC is assumed to be sinusoidal.

14 12

THD (%)

10 8

5.1. Scenario A: adequate APLC capacity

6

In this scenario, it is assumed that the installed capacity of APLCs is adequate for harmonic compensation in the MG. The simulation cases are as:

4

• Case I: Just APLCs participate in harmonic compensation. • Case II: All APFs participate in the market and are online for harmonic compensation. • Case III: All APFs could participate in the market by the selection of

2 0 0

5

10

15 Bus

20

25

30

the MG operator.

Fig. 12. THD level without compensation.

Note that no possible working in LOC region is considered in this scenario due to adequate APLC harmonic capacity.

other APF resources. Hence, ratings of these APFs are greater than the ratings of other APF resources shown in Table 4. The APLS ratings are equal to 0.32 pu and 0.26 pu for APLCs at bus #2 and bus #9, respectively. The proposed HPM framework is validated in two different scenarios each one includes some various simulation cases. In scenario A, it is assumed that adequate harmonic filtering capacity is available by the installed APLCs. Hence, MG operator could use other APF resources to decrease the total cost of distortion power procurement. In scenario B, harmonic compensation capabilities of APLCs are not adequate for the satisfaction of the harmonic standards. Hence MG operator could use other available APF resources in order to keep the THD of voltage buses in desired levels. APF resources are supposed to submit their four components of offer prices (π0, π1, π2, π3). The offer prices are also shown in Table 4. The lower and upper bounds of voltage are taken 0.95 pu and 1.05 pu, respectively. Harmonic power market problem (in

5.1.1. Case I In this case, just APLCs participate in harmonic compensation. The APLCs should be capable to individually mitigate harmonic distortions without using other APFs. Hence, due to the high rating of the APLCs, availability cost and cost of losses are high compared to other APFs as shown in the last columns of Table 4. The results of the HPM for this case are shown in Table 5. Individual harmonic injections and total current injections of the APFs are represented in Table 5. APLC #2 is more participated in the HPM compared to APLC #1. Provided distortion power is equal to 0.386 pu which, 0.219 pu (almost 72%) of that is supplied by the APLC #1. Various terms of distortion correction powers are also shown in Table 5. A big portion of the provided distortion power is for current distortion power. Voltage distortion power is equal to zero which could be a result of zero injection in fundamental

Table 5 HPM results, scenario A. Case 1

Case II

Case III

APFs

1

2

1

2

3

4

5

6

1

2

3

4

5

6

I1 (pu) I5 (pu) I7 (pu) I11 (pu) I13 (pu) I17 (pu) I19 (pu) I (pu) DI (pu) DV (pu) DH (pu) D (pu) Revenue ($/h)

0 0.021 0.158 0.023 0.015 0.027 0.031 0.167 0.166 0 0.001 0.166 41.0

0 0.095 0.179 0.066 0.036 0.047 0.047 0.219 0.219 0 0.011 0.220 62.2

0 0.005 0.015 0.004 0.003 0.004 0.004 0.017 0.017 0 0 0.017 17.7

0 0.041 0.070 0.022 0.013 0.020 0.020 0.090 0.087 0 0.002 0.087 25.6

0.016 0.007 0.009 0.003 0.020 0.003 0.003 0.013 0.012 0.004 0 0.013 4.7

0.022 0.002 0.005 0.002 0.001 0.001 0.002 0.006 0.006 0.004 0 0.007 7.2

0.015 0.004 0.012 0.002 0.002 0.003 0.002 0.014 0.014 0.002 0 0.014 5.7

0.107 0.033 0.107 0.030 0.019 0.028 0.030 0.125 0.122 0.004 0.002 0.122 14.7

0 0 0 0 0 0 0 0 0 0 0 0

0 0.051 0.085 0.026 0.016 0.024 0.025 0.110 0.107 0 0.002 0.107 29.0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0.107 0.034 0.107 0.029 0.018 0.028 0.030 0.125 0.122 0.004 0.002 0.122 14.7

Total Cost ($/h)

103.2

75.8

43.7

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APFs with lower offered prices, could successfully decrease operational cost of MG for reducing harmonic distortions

5.5 5

Case I Case II Case III

4.5 4

5.1.3. Case III This simulation case is similar to the previous one, except that there is no obligation for participating all APFs in the HPM. The MG operator could choose among various APF resources to economically satisfy harmonic standard levels. The APFs could be offline by setting the binary variable of w1f to zero. The results of the HPM are shown in Table 5. Obviously, APLCs #2 and #6 are just selected for harmonic compensation which is the most optimal combination for online APFs. Required harmonic compensation currents for each harmonic order and total reference currents of the APFs are shown in Fig. 15. For APF #2, current injection for fundamental frequency is zero since the APLC just inject harmonic compensation currents to the MG. Total reference currents for the APFs are also shown in this figure. The HPM could successfully determine harmonic compensation currents in each harmonic order for each APF. Total costs of harmonic compensation in all simulation cases are shown in Fig. 16. As it is obvious, total compensation cost in case III is reduced to 43.7 $ which shows a 58% reduction compared to the case I and 42% reduction compared to the case II. This could bring a great saving for MG operator to meet the harmonic related standards in the network. The THD desired level for this case is shown in Fig. 13 as well. THD trends in both cases I and II are similar as shown in Fig. 13. This could be the result of dominating harmonic compensation provided by APFs #2 and #6 in both simulation cases.

THD (%)

3.5 3 2.5 2 1.5 1 0.5 0 0

5

10

15 Bus

20

25

30

Fig. 13. THD level with compensation in scenario A.

frequency. Effects of APLCs in compensation of harmonic distortion to the desired level of THD are shown in Fig. 13. The total cost of supplying distortion correction power from APLCs is equal to 103.2 $. Although offered prices of APLC #2 is more than APLC #1, payments to this APF is more. This shows the efficacy of the APF location in harmonic compensation. This brings a 62.2 $ revenue for APLC #2 for participating in the harmonic power market. It is about 60% percent of total payments to the APF resources in the market.

5.2. Scenario B: inadequate APLC capacity

5.1.2. Case II In this case, all APF resources are participating in the HPM. It is assumed that all APFs are now online and should be employed by the MG operator. Hence, Active and reactive powers and, maximum available distortion powers of DER based APFs are also shown in Table 4. The results of the HPM for this case are also shown in Table 5. Total required distortion correction power to keep THD level is equal to 0.265 pu. It shows about 32% decrease compared to the previous case. This may be a result of various locations of APFs which bring an opportunity to deliver harmonic compensation currents in more buses. Therefore, it is not required to flow the harmonic compensation currents in the whole of the network compared to the central compensation mechanism. Individual distortion powers of APF resources are shown in Fig. 14. APFs #6 and #2 are the main sources of the supplied distortion correction power. This could be due to their location and their bids for the cost of losses shown in Table 4. DFIG (APF #6) is loaded to the maximum available distortion power capacity for 0.125 pu. THD level of buses voltages is also shown in Fig. 13. Proper THD level is archived using extra APF resources. As shown in the last row of Table 5, total compensation cost is reduced to 75.8 $ which shows about 27% decrease in total cost compared to the case I. Hence, using DER based

In scenario B, the harmonic filtering capacity of APLCs is supposed to be not adequate for mitigation of all harmonic distortions. Hence, it is necessary to use other APF resources for harmonic standards satisfaction. All nonlinear loads were multiplied by a scale factor to increase levels of harmonic distortion in the MG. Some simulation cases are provided here for representing possible working in the LOC region. In cases I, II, and III, nonlinear loads were multiplied by a scale factor of 1.25. The results of their HPMs are shown in Table 6. In case I, the THD level is equal to 6.1% which is more than the standard level. Both APLCs are fully loaded and there is not adequate capacity for harmonic filtering in the MG. Total cost is equal to 185.1 $ in this case, however, the THD level is above the standard criterion. Installing some new APLCs could be a possible solution which obviously imposes significant costs to the MG operator. In case II, other DER based APFs are participating in the HPM. It is assumed that all APFs are online similar to the previous scenario. Results of case II is also represented in Table 6. As it could be seen, the THD constraint is satisfied with respect to the harmonic standard of 5%. The total cost is also equal to 111.4 $ in this case, which shows a 40% decrease in the total cost of harmonic compensation in the MG. Distortion correction power loadings of various APF resources are shown in Fig. 17 for this case with normalized values. Supplied distortion power of the APF is normalized by the available distortion power capacity in Table 4. Almost all DER based APFs are loaded at their maximum capacity. This could be a result of their fewer price bids for the cost of losses. Hence, employment of APF resources based on DERs could bring a great saving for the satisfaction of harmonic standards in the MG. In the third case, the online status of APF is determined based on the MG operator requirements. The results of the HPM are also represented in Table 6. As it could be observed, the desired THD level is satisfied with employing just three APFs; APF #2, APF #5, and APF #6. Hence other APFs could be ignored for providing distortion correction power. This may decrease the total cost of the HPM to 96.9 $. It shows about a 48% decrease in operation cost compared to case I. Total operation costs for all three cases in scenario B are shown in Fig. 18. Decreasing total cost by employing DER based APFs are obviously shown in this

Fig. 14. Individual supplied distortion power of APF resources, Case II, Scenario A. 928

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h1

h5

h7

h11

h13

h17

h19

Reference Current

0.2 APF #2 0.1

Current magnitude (pu)

0

-0.1

-0.2 0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.4 APF #6 0.2 0 -0.2 -0.4 0

0.002

0.004

0.006

0.008

0.01 t (sec)

0.012

0.014

0.016

0.018

0.02

Fig. 15. Harmonic and total reference currents of accepted APFs in the HPM, Case II, Scenario A.

100

120 Distortion power loading (%)

90

Total Cost ($)

100 80 60 40 20

80 70 60 50 40 30 20 10

0

Case I

Case II

0

Case III

APF #1

APF #2

APF #3

APF #4

APF #5

APF #6

Fig. 16. Total cost of harmonic compensation, Scenario A.

Fig. 17. Distortion power loading of APFs in case II, Scenario B.

figure. The HPM could successfully satisfy harmonic standards with respect to the minimum operation cost in the MG. Finally, in two extra simulation cases, the ability of DER based APFs in increasing harmonic load-ability of the MG was investigated. In cases IV and V, harmonic load demands was increased gradually until the point of violation of the THD constraint. A scale factor parameter is used to represent the amount of increment in load demands of the MG.

The results of these two cases are represented in Table 7. In case IV, all APFs are online without possible working in the LOC region. The scale factor for nonlinear load increment was determined to 1.297 pu in this case. Total cost is equal to 131.1 $ for the satisfaction of the THD level of 5%. Similar to case II, all DER based APFs are loaded to their maximum values. In case V, the maximum harmonic load-ability of the MG considering the LOC operation was determined. The scale factor for

Table 6 HPM results, scenario B. Scale (pu) Operation

Case I 1.25 APLCs

Case II 1.25 All APFs online, No LOC region

Case III 1.25 All APF, No LOC region

APFs

1

2

1

2

3

4

5

6

1

2

3

4

5

6

I (pu) D (pu) Revenue ($/h) THDmax (%)

0.322 0.320 105.5 6.1

0.269 0.260 79.7

0.062 0.062 20.7 5.0

0.217 0.210 58.3

0.013 0.013 4.7

0.020 0.021 7.4

0.014 0.014 5.7

0.125 0.122 14.7

0 0 0 5.0

0.262 0.253 75.5

0 0 0

0 0 0

0.014 0.014 5.7

0.125 0.122 14.7

Cost ($/h)

185.1

111.4

96.9

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Harmonic filtering capability

200 180

Total Cost ($)

160

LOC region

140 120 100

All APFs, no LOC

80 60

Harmonic loads (pu)

APLCs

40 20 0

Case I

Case II

1 .0 6 5

Case III

1.2 9 7

1 .3 7 8

Fig. 19. Harmonic filtering capability of the MG.

Fig. 18. Total cost of harmonic compensation, Scenario B.

However, they are nonlinear which may increase harmonic levels in the MG. If considerations are not watched out, some problems may be raised about the quality of the delivered power to the consumers. Meanwhile, customers are going to be more concerned with the quality of power they paid for. If the utilities do not mind about the PQ, their revenues may be decreased. The obligations of competitive markets reveal the necessity to improve the quality of power as a product in the power markets for retailers. In this paper, an optimization based HPM was proposed for central management of APF resources in the MG. A detailed review of various APF resources was performed to model APFs for participating in the HPM. Furthermore, a distortion correction power expected payment function was proposed for APFs to cover imposed costs of harmonic mitigation activities. The HPM model and related constraints were introduced as an optimization model for the optimal coordination of APFs. The proposed model was validated in various simulation cases. As it was shown, the proposed model could successfully determine the harmonic compensation actions of APFs to economically satisfy harmonic standards of the MG. Besides, it was shown that current distortion power contributes a large part of distortion power compared to the voltage and harmonic distortion powers. DER based APFs could extensively increase harmonic filtering capacity of the network since they could operate as an APF. Working in LOC region could also introduce extra filtering capacity. Regards to the proposed model, the following discussions are represented:

load increment was determined to the point of 1.378 pu in case V. Possible working in the LOC region increases harmonic load-ability from 1.297 pu to 1.378 pu. It shows about a 6.25% increase in harmonic filtering capability with respect to the 10% allowed deviation in the active and reactive powers of DERs. Active and reactive power adjustments are also represented in Table 7. The power adjustments are contributed to increasing total compensation cost which is equal to 198.5 $/h for this case. Harmonic filtering capability of various harmonic loading conditions of the network with respect to the APF operation strategies is shown in Fig. 19. APLCs could mitigate harmonic distortion until to the scale factor of 1.065 pu. After that, harmonic load-ability could be increased from scale factor of 1.065 pu to the 1.297 pu using DER based APFs. It shows about a 22% increase in harmonic load-ability. Working in LOC region may also increase extra 0.081 pu in harmonic load-ability as shown in Fig. 19. These two possible operation strategy of APFs, could bring more distortion correction power capability for the MG. It could defer requirements for installing new APLCs for harmonic mitigation purposes. It was shown in this section that the proposed HPM could establish an economic reliable framework for the management of harmonic compensation activities in the MG. It could manage participation of various-owner APF resources in the MG to satisfy harmonic standards. It should be noted that harmonic mitigation is just one of the main power quality issues and has been considered in this paper. Other power quality problems could also be mitigated by similar frameworks for reliable coordination of DER based filters. Reducing total compensation costs, increase in harmonic load-ability of the network and defer requirements for installation of new filters could be accounted as the main benefits of the HPM.

• Various APF resources based on DERs bring a great capability for

6. Discussions

• •

Future smart MGs are facing with a large variety of loads with PE interfaces due to their great flexibility and controllability. It has been expected that about 60% of future loads are of such PE based loads.

mitigation of harmonics in the MG. In fact, many ancillary services could be taken from DERs as it was mentioned in the paper. These provide great flexibility for both DER owners and MG operator to cope with network related issues and standards. This paper is focused on harmonic filtering capability of the DERs. The HPM is proposed as a quality service for management of harmonic mitigation activities. The MG infrastructures may provide essential requirements for the implementation of the HPM. Various DERs are distributed in the

Table 7 Harmonic load-ability of the MG, scenario B. Scale (pu) Operation

Case IV 1.297 All APFs, No LOC region

Case V 1.378 All APFs, With LOC region

APFs

1

2

3

4

5

6

1

2

3

4

5

6

I (pu) D (pu) Δp (pu) Δq (pu) Revenue ($/h) THDmax (%)

0.134 0.133 0 0 32.7 5.0

0.236 0.229 0 0 65.9

0.013 0.013 0 0 4.7

0.020 0.021 0 0 7.4

0.014 0.014 0 0 5.7

0.125 0.122 0 0 14.7

0.294 0.292 0 0 91.1 5.0

0.259 0.250 0 0 74.9

0.014 0.014 0.0006 0.0004 4.7

0.021 0.021 0.0004 0.0002 7.4

0.014 0.014 0.0002 0.0001 5.8

0.128 0.126 0.003 0.002 15.1

Cost ($/h)

131.1

198.5

930

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•

•

network. Communication links are provided to ensure data management in the MG, the MG control center manages the MG realtime operation, and smart meters are used for measurements. Therefore, the requirements for the HPM are available in the MG. One of the main advantages of the proposed model is its scalability. It means that any new APF devices may easily be imported into or omitted from the market. Hence, there is no need to change the control architecture for new APFs. Moreover, distributed compensation reduces the working stress on the APFs. This redundancy increases the reliability of the compensation model. Since the DERs are not necessarily owned by the MG operator, investigations about the market and legal issues should be carried out to distinguish various aspects of such compensation activities.

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