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The frequency-independent control method for distributed generation systems
Applied Energy 96 (2012) 272–280
Contents lists available at SciVerse ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
The frequency-independent control method for distributed generation systems Siamak Naderi a, Edris Pouresmaeil b,⇑, Wenzhong David Gao c a
Faculty of Azad University, Isfahan, Iran Centre d’Innovació Tecnológica en Convertidors Estátics i Accionaments (CITCEA-UPC), Departament d’Enginyeria Eléctrica, Universitat Politècnica de Catalunya, ETS d’Enginyeria Industrial de Barcelona, Barcelona, Spain c Department of Electrical and Computer Engineering, University of Denver, Denver, CO, USA b
a r t i c l e
i n f o
Article history: Received 6 July 2011 Received in revised form 27 August 2011 Accepted 18 September 2011 Available online 3 November 2011 Keywords: Distributed energy resources Distributed generation Hysteresis current control Reactive power compensation Rotating synchronous reference frame Voltage source inverter
a b s t r a c t In this paper a novel frequency-independent control method suitable for distributed generation (DG) is presented. This strategy is derived based on the abc/ab transformation and abc/dq transformation of the ac system variables. The active and reactive currents injected by the DG are controlled in the synchronously rotating orthogonal dq reference frame. The transformed variables are used in control of the voltage source inverter that connects DG to distribution network. Due to importance of distributed resources in modern power systems, development of new, practical, cost-effective and simple control strategies is obligatory. The new control method of this paper does not need a Phase Locked Loop (PLL) in control circuit and has fast dynamic response in providing active and reactive power to nonlinear load. From extensive simulation results, high performance of this control strategy in DG application is demonstrated with improved voltage profile, increased power factor and reduced total harmonic distortion. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Nowadays, energy technologies have a central role in social and economic development at all scales, from household and community to regional, national and international. Among its welfare effects, energy is closely linked to environmental pollution and degradation, economic development and quality of living [1]. Today, we are mostly dependent on nonrenewable fossil fuels that have been and will continue to be a major cause of pollution and climate change. The necessity of producing more energy combined with the interest in clean technologies yields in an increased development of power distribution systems using DG resources based on renewable energy sources. DG technologies include photovoltaic, wind turbines, fuel cells, small sized micro turbine packages, stirling-engine based generators and internal combustion engine-generators. These technologies are entering a period of rapid expansion and commercialization [2]. Perhaps the greatest challenge in realizing a DG future is to develop this technology for integration and control of renewable energy sources in smart grid distributed generation [3]. The smart power grid distributed energy system would provide the platform for the use of renewable sources and adequate emergency power for major metropolitan load centers and would safeguard in preventing the complete blackout of the interconnected power systems due to man-made events and environmental calamity and would provide the ability to break up the interconnected ⇑ Corresponding author. Tel.: +34 93 401 67 27; fax: +34 93 401 74 33. E-mail addresses: [email protected] (E. Pouresmaeil), Wenzhong. [email protected] (W.D. Gao). 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.09.034
power systems into smaller cluster regions [4,5]. As a result, a new simple low cost and practical control method is necessary for interconnection of DG resources to the distribution grid [6,7]. Several control techniques and strategies have been proposed and reported for interconnection of DG resources to the grid. In Ref. [8] an overview of control and grid synchronization algorithms, and their role and influence in the control of a DG system on normal and faulty grid condition were discussed. Different hardware structures like dq and stationary and natural frame control structures were presented and their major characteristics were pointed out. A discussion about different controllers for the grid-side converters, and their ability to compensate for low-order harmonics presented in the utility grid was given and four different control methods that a DG system can use during an unbalanced grid fault were discussed. In Ref. [9], a nonlinear control technique is proposed to enhance the dynamic performance of shunt active power filter which is modeled in the dq frame. NPC voltage source inverter (VSI) is proposed as the interfacing system of DG resources and AC grid. The exact feedback linearization theory is applied in the design of the controller. This control strategy allows the decoupling of the currents and enhances their tracking behavior and improves the DC-voltage regulation. In Ref. [10], a dual inverter is proposed for connection of wind energy to the grid. One of the two inverters in the dual inverter is connected to the rectified output of the wind generator while the other is directly connected to a battery energy storage system. This approach eliminates the need for an additional dc–dc converter and thus reduces power losses, cost and complexity. The main issue with this method is uncorrelated dynamic
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changes in dc-link voltages that results in unevenly distributed space vectors. Several other control strategies for interfacing system between different types of supplies based on renewable and non-renewable energy resources and electrical networks are proposed and presented for different objectives [11,12]. In all the proposed methods, a solution has been proposed for an important problem in electrical networks. This paper presents the theoretical development of a multi-objective control technique of VSI which considers different aspects of electrical network during integration of DG resources to the electrical grid. DG system can be connected to the network in series or shunt type. Shunt connection injects current at Point of Common Coupling (PCC), while series connection injects a voltage between the utility supply and the customer load. Because the compensated quantities (reactive power or harmonics) are related to the current, shunt type is more realistic as it injects current at PCC [3,13]. Fig. 1 shows the shunt connection of a DG system to the distribution network. Current controlled voltage source inverter (VSI) is proposed for interfacing between DG and distribution networks, because of its fast dynamic response, accurate performance, ease of implementation and its inherent closed loop control for the current to guarantee the required operating point [14,15]. The command signal for the VSI which is current signal in nature will include the information of active power supplied from DG system and reactive power required to compensate the voltage fluctuation at load-side PCC or total reactive power compensation and also harmonic currents. When interfaced to the grid with the auxiliary help of a battery to supply the transient need of power, the details on the distributed source behavior tend to lose importance when looking at the performance of the unit as seen from the grid terminals. Indeed, the VSI will be connected to the terminals of the battery and will only see a relatively stiff DC voltage. The power source no longer has a dramatically fast transient response, since its only task is to keep the battery charged. So, in this paper we look at the DG system as an inverter connected to a battery. This simplification makes the design and analysis of the power electronic interface less burdensome. The performance of the proposed system is simulated using Matlab/Simulink. The results are discussed to demonstrate the potential of the proposed technique.
1.1. Frequency independent control technique The current control techniques of VSI presented in this paper is based on analysis of voltage and current vector components mainly in a special reference frame with mathematical equations and transformation matrices [16]. To decompose voltage and current components in a rotating reference frame, calculation of instantaneous angle of voltage or current is needed. To obtain this angle,
VS
RS
LS i s
PCC
ic
il
Phase-Locked Loop (PLL) is commonly used in voltage source inverter’s control loop [17–19]. Employing of phase locked loop has some disadvantages such as problems due to synchronization of DG with the grid and elimination of a wide range of frequencies which is not favorable in DG’s application as an active power filter. In addition, PLL is very sensitive to noises and disturbances [20]. In frequency-independent control algorithm instantaneous angle of load voltage is calculated directly by decomposing voltage vector components in a rotating reference frame. Removing PLL from control circuit of voltage source inverter introduces a new control method for DG systems. In this control strategy synchronization problems will be resolved and dynamic response of DG will be improved. This control technique can: provide load active power, compensate load reactive power and track rapid variations in load reactive power, supply load harmonic currents. In consequence of these characteristics, DG can also compensate load voltage sags. 1.2. Voltage and currents in rotating and stationary reference frame, calculation of reference current of DG control system Voltages and currents of nonlinear DG link are shown in Fig. 2. To achieve frequency-independent control, voltage and current components are obtained in a stationary reference frame, i.e., in ab components by the following equation: !
v ¼ TV!and
!
i! ¼ TI
ð1Þ
where v , T, V, i and I are defined as:
2 3 rffiffiffi va 2 1 1=2 1=2 6 7 pffiffiffi pffiffiffi ; V ¼ 4 v b 5; v ¼ avb ¼ 3 0 3=2 3=2 vc 2 3 ila ! ia 6 7 i ¼ and I ¼ 4 ilb 5: ib ilc !
!
va T¼ vb
It is noted, in the three-wire systems with balanced load zero sequence component of voltage is null and therefore zero sequence current component is also null. In the next stage, injected current components of DG system to the grid must be calculated in ab frame. For this purpose, ab frame is transformed to synchronously rotating reference frame, i.e., in dq components. In this transformation d-axis vector is in direction of voltage vector. With this consideration, vertical component of voltage (q-component of Vs
Rs
Ls
is
SW
PCC
il
Utility Load
Current Filter
Load
ic
il
T T
VSI
vab,vbc
ic
VSI & Current Controller
C
DC/AC
vdc
ic*
DG Source Fig. 1. Shunt connection of a DG system to the grid.
Reference Generator Fig. 2. Voltage and current of nonlinear link.
DG
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Pref is the power that DG system must provide in fundamental fre quency. icd h1 is the d-component of DG link reference current in fundamental frequency. Due to limited output power of voltage source inverter, reference current must be restricted. Calculation of d-component of reference current with this method makes it possible to control maximum active power delivered to the grid by changing Pref. Pref depends on DG system capacity, capacity of power electronic devices and transformers. 1.3. Calculation of harmonic components of d-axis reference current Calculation of load current in dq reference frame by 5 makes it possible to separate fundamental and harmonic currents. ild can be separated into DC and alternative components as:
ild ¼ ild þIld
ð9Þ
Fig. 3. Voltage and current components in stationary and rotating synchronous reference frame.
voltage) in rotating synchronous reference frame is always zero (vq = 0) [3]. Fig. 3 shows the voltage and current components in stationary and rotating synchronous reference frames. Transformation matrix which is based on Park’s equations is given in the following equation:
ild ilq
¼
Cosh
Sinh
Sinh Cosh
ila
ilb
ð2Þ
where ild and ilq are direct and quadrature components of current in rotating synchronous reference frame respectively; h is instantaneous angle of load voltage. By Fig. 3, h can be calculated as:
h ¼ tan1
vb : va
ð3Þ
According to Fig. 3, d-component of voltage in stationary and rotating synchronous reference frame can be calculated as: !
!
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
v d ¼ j v dq j ¼ j v ab j ¼ v 2a þ v 2b :
ð4Þ
By (2)–(4) can be rewritten as [21]:
ild
ilq
¼
1
vd
v a v b ila v b v a ilb
ð5Þ
By 5, d and q-components of current in rotating synchronous reference frame can be calculated by means of current components in stationary reference frame. In rotating reference synchronous frame, quadrature component of load current is perpendicular to direct component of voltage (vd\ilq). So q-component of load current indicates required reactive power of the load. To compensate load reactive power, DG must provide a current with q-component equal to ilq. For this purpose, it is sufficient to set q-component of reference current of DG equal to q-component of the load current as shown in the following equation:
icq ¼ ilq
ð6Þ
ild is alternative d-component of load current in rotating synchronous reference frame which is related to harmonic components of load current and Ild is the DC term of load current in this frame which is related to fundamental frequency of load current. To compensate harmonic current it is necessary to separate alternative and constant components. For this purpose, a high pass filter must be used. To minimize the influence of the HPF’s phase responses, by means of a low-pass filter (LPF), a minimal phase HPF (MPHPF) can be obtained, the transfer function of this LPF has order and cutoff frequency as the same as HPF. So, the minimal phase HPF can be obtained simply by the difference between the input signal and the filtered one, which is equivalent to performing: HMPHPF(s) = 1–HLPF(s). A double-precision filter using the Chebyshev type-II fifth order low-pass filter is used for this purpose. Fig. 4 depicts amplitude and phase of high pass filter and minimum phase high pass filter. The filter considered has a cut-off frequency fc ¼ 2f (f = 50 Hz) which promises the extraction of DC components in the nonlinear load currents. So, harmonic components of load current at d-axis are obtained. To use distributed generation as active filter, harmonic components of load current must be supplied by DG. For this purpose, vertical component of nonlinear link reference current is obtained by 6 and DC component of reference current is calculated from:
where is calculated by 8. Equivalent reference currents in stationary reference frame are obtained by:
"
ica
¼
Pref
vd
vd
va vb
v b
"
icd
va
icq
# ð11Þ
:
2
ic
3 " # ica ica 6 7 ¼ 4 icb 5 ¼ T1 : icb icc
ð12Þ
For implementation, 1 can be rewritten based on line voltage
v¼
pffiffiffiffiffiffiffiffi 1 1=2 v ab pffiffiffi : 2=3 0 3=2 v bc
ð13Þ
By substituting 1 in 2 and considering ilc = (ila + ilb):
ild ilq
ð8Þ
1
By 1 and calculating inverse matrix, reference current in abc frame are achieved as:
!
icd h1
¼
P ¼ v d :icd
ponent of DG Link current. d-component of DG link reference current to provide active current in fundamental frequency can be calculate by 7. So we have:
#
icb
as:
vd is load voltage in fundamental frequency at the PCC icd is d-com-
ð10Þ
h1
icd h1
icq is the vertical component of DG link reference current that is shown in Fig. 2. By this consideration, total load reactive current is compensated. The active power injected from DG system to the grid is:
ð7Þ
icd ¼ ild þicd
¼
pffiffiffi Sinðh þ p=3Þ SinðhÞ ila 2 : Cosðh þ p=3Þ CosðhÞ ilb
So, by 12, 14 and icc ¼ ðica þ icb Þ:
ð14Þ
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Phase (degree)
Magnitude (dB)
0
MPHPF
-50
HPF
-100 -150 360 315 270 225 180 135 90 45 0 -45 0 10
HPF
MPHPF 1
2
10
10
3
10
Fig. 4. Amplitude and phase of high pass filter and minimal phase high pass filter.
"
ica
icb
# ¼
pffiffiffiffiffiffiffiffi 2=3
CosðhÞ
SinðhÞ
Cosðh þ p=3Þ Sinðh þ p=3Þ
"
icd
icq
# ð15Þ
h is calculated from 3. Eqs. 14 and 15 indicate Park transformation and its inverse respectively. Separation of current components into alternative and DC terms provide proper currents for voltage source inverter, introducing a flexible distributed generation with following characteristics: Compensation of harmonic currents (active filter). Compensation of harmonic currents and load reactive power (active filter and distributed static compensator). Compensation of harmonic currents and load reactive power and providing active power (DG system).
Fig. 5 shows the diagram of DG control system for harmonic compensation, reactive power compensation and active power control. 1.4. Current controller of voltage source inverter Many current control methods for three phase systems are presented in [22]. Among them, current control using hysteresis regulators are widely used. Some of the advantages of hysteresis current control (HCC) are: simplicity in implementation, high speed of current loop, independency from load parameters.
Fig. 5. Diagram of DG control system for harmonic compensation, reactive power compensation and active power control.
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2. Simulation results To describe and validate proposed control method, simulations are carried out for a distribution network connected with a nonlinear DG link in Matlab/Simulink environment. Its single-line diagram and principle of proposed control system are shown in Figs. 1 and 5 respectively. Simulation parameters are given in Table 1. It is considered that for the whole period of simulations a full-wave thyristor converter is fed by the main source. During simulation process active power which is delivered from DG link is considered constant. This assumption makes it possible to evaluate the capability of DG link to track the fast change in the reactive power, independently. To simulate a real distribution network, the loads are connected and disconnected to distribution network randomly
Fig. 6. Hysteresis current control (a) closed loop control and (b) switching technique demonstration.
Fig. 6 demonstrates the basic control algorithm of the current controlled VSI. HCC in nature is a closed loop control for the current of VSI. Comparison of the calculated reference currents and the actual DG injection currents generated by the VSI will result in the error signal (e in Fig. 6a), which controls the switches of the inverter. When the error reaches the upper limit of the hysteresis comparator, IGBTs (Insulated Gate Bipolar Transistor) are switched ON to increase the current; and when the error reaches the lower limit, the current is forced to decrease by switching the IGBTs OFF, Fig. 6b. These operations lead to the fast dynamic response that characterizes HCC among other current control techniques. The range of the error signal, h, directly controls the amount of ripples of the output current from the VSI and is called the hysteresis band. The current is forced to stay within these limits even while the reference current is changing. The switching frequency is altered by the width of the hysteresis band, the size of the inductor that the current flows through (Lc in Fig. 6) and the DC voltage (vdc) applied from the DG to the VSI. A practical method to calculate inductor value for current filter in nonlinear link is presented in [23]. According to this method, filter inductor is calculated by:
Lc ¼
2v dc 9hfsw:max
ð16Þ
where vdc is DC bus voltage, h is the hysteresis band, fsw.max is maximum switching frequency. From 16, maximum switching frequency can be calculated. This frequency is related to DC bus voltage and inversely related to hysteresis bands and filter inductor. By increasing switching frequency, output current ripple and the distortion of voltage and current at PCC are decreased. On the other hand, by increasing switching frequency, electro-magnetic interference and switching losses occur and high speed converters and comparators are needed.
Fig. 7. (a) Load current, nonlinear link current and source current before and after DG connection and before and after additional load connection and (b) d and qcomponents of load.
Table 1 Specification parameters. Vs (rms)
fs (Hz)
Rs (X)
Ls (H)
Rc (X)
Lc (H)
vdc (V)
h
Pload (kW)
Qload (kvar)
380
50
0.05
0.001
0.1
0.04
1000
±1
9
6
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277
and Total Harmonic Distortion (THD) of current waveform are calculated and compared with each other in various conditions. Since the principle of proposed current control technique is based on separating active and reactive current components in rotating synchronous reference frame (dq components), in all conditions d and q-component of load current are shown. To demonstrate the ability of nonlinear DG link to compensate whole reactive power, load voltage, load current and source current are shown in one figure simultaneously. The following subsections present the process of simulation for connection and disconnection of different kind of loads. 2.1. Connection of DG link to the distribution network and harmonic load increment The nonlinear DG link is connected to the network at t = 0.05 s. This process is continued until t = 0.15; at this moment another full-wave thyristor converter similar to the prior load is added to PCC and it is removed at t = 0.3 s. Figs. 7–9 shows the related currents, load voltage and current spectra, respectively. After connection of DG link the source current becomes zero and all the active and reactive current component including fundamental and harmonics frequency are provided by DG link, as shown in Fig. 7a. Reference currents during period of connection of DG link to the network are shown in Fig. 7b. The load current is fed from nonlinear link continuously until connection of additional load to the network. As shown in Fig. 8a, after connection of additional load, production in control circuit of DG system is delayed for one cycle. This is due to settling time of MPHPF filter. After the transient times, the load voltage and source current are in phase and source does not need to provide reactive and harmonic currents for the load which
Fig. 9. Currents spectra. (a) Load current spectra before connection of DG link to the network. (b) Load current spectra after connection of additional load and (c) Source current spectra after connection of additional load.
is shown for phase a. With the same delay as before, additional load is removed at t = 0.3 s. After the pass of the transient times the source current becomes zero. As shown in Fig. 8, load harmonic currents are provided by DG and source current is sinusoidal but there are sharp edges on current waveforms which are related to high order harmonic frequencies and created during switching of thyristor converters. To evaluate the capabilities of DG link to compensate harmonic currents, the spectra of currents before and after connection of DG link and after connection of additional load are shown in Fig. 9. Fig. 9a shows that before connection of additional load the THD is 21.8%. After connection of additional load this value is 21.91%, as Fig. 9b indicates. Fig. 9c shows that the THD of source current after connection of additional load is just 5.86%. The comparison between this information demonstrates capabilities of DG link to compensate harmonic currents of the load. 2.2. Linear load increment Fig. 8. Source current, load voltage and load current (a) before and after connection of additional load and (b) before and after disconnection of additional load.
In this section, to evaluate DG link to track both harmonic and sinusoidal currents the RL load is connected to PCC at t = 0.4 s
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and it is removed at t = 0.55 s. The related simulation results are shown in Figs. 10–13. Additional load is a resistive-inductive load. Maximum delivered power from DG system is considered constant (Pref = 8 kW). Considering that all required reactive power of additional load is provided by DG system, additional required load active power must be provided by main source. Fig. 10a shows load current, source current and nonlinear link current during load increment. At t = 0.4 s, an extra load is connected to the distribution network and due to delay settling time of MPHPF filter, production in DG link circuit is started 0.02 s after load connection. According to Fig. 10a, load harmonic current is provided by DG and source current is sinusoidal. The reference currents in dq frame, which are equal to d and q-components of the load current, are shown in Fig. 10b. The step response of the MPHPF which causes the delay in the control circuit of DG link is apparent from this shape. After production in DG link control circuit, load voltage and source current become in phase which is shown for phase a in Fig. 11a. So, source does not provide reactive components. The
Fig. 11. Source current, load voltage and load current (a) before and after connection of additional RL load and (b) before and after disconnection of additional RL load.
Fig. 10. (a) Load current, nonlinear link current and source current before and after additional RL Load connection and disconnection and (b) d- and q- components of load.
Fig. 12. Currents spectra after connection of additional RL load. (a) Load current spectra and (b) source current spectra.
S. Naderi et al. / Applied Energy 96 (2012) 272–280
279
Fig. 14. Source, load and DG link (a) active power and (b) reactive power.
Fig. 13. (a) Load current, nonlinear link current and source current before and after disconnection of additional RL load and (b) d and q-components of load.
additional RL load is removed at t = 0.55 s. As shown in Fig. 11b, after the pass of the transient times the source current become zero. Fig. 12a shows the THD after connection of additional RL load to the distribution network is 10.89%. Fig. 12b shows that the source current THD in this period is just 2.91% which illustrates the potential of DG link to compensate considerable amount of harmonic frequencies. After disconnection of additional RL load at t = 0.55 s, as shown in Fig. 13, the load, DG link and source currents return to their prior values. It is noted that all voltage and current waveforms vary within the hysteresis band. Finally, the active and reactive powers which pass through network are shown in Fig. 14. Fig. 14a shows source, load and DG link active power during connection of DG link and connection and disconnection of extra loads. As one can predict, the waveform of active power of DG link contains a step response which is related to MPHPF. So, the delay and swings in this wave are due to the same reasons mentioned above. In addition, after connection of DG to the network the active power which is delivered from source is decreased to zero and DG link delivered active power, completely tracking load active power. Due to delay settling time of MPHPF, after connection of additional
load at t = 0.15 s, some swings appear in active power waveform. The transient time takes one cycle (0.02 s). The rate of changes in active power of DG has fast slope at t = 0.05 s. That is due to, before connection of distributed generation link, the DG control circuit has some information about the nature of load. Fig. 14b indicates source, load and DG link reactive power. As there is no filter in the control loop of q-component of DG link reference current, the waveform of DG reactive power has better response than DG’s active power response. This Figure also shows the capability of DG system to track and compensate load reactive power, completely. This can prevent load voltage fluctuations in case of sudden change in load reactive power. 3. Conclusions In this paper, a frequency-independent control technique for distributed generation resources has been presented. Due to sensitivity of PLL to noises and distortion, its elimination can bring benefits for robust control against distortions in DG applications. Also, the problems due to synchronization between DG and network do not exist and DG link can be connected to the distribution network without any current overshoot. One other advantage of proposed control method is its fast dynamic response in tracking reactive power variations; the control loops of active and reactive power are considered independent. By the use of proposed control method, DG system is introduced as a new alternative for distributed static compensator in distribution network. Simulation results illustrate that in all conditions the load voltage and source current are in phase and so, by improvement of power factor at PCC, DG systems can act as power factor corrector devices. The simulation results indicate that proposed DG system can provide required harmonic load currents in all situations. So, by reducing THD of source current it can act as an active filter. The proposed control method can be used for different types of DG resources as power quality improvement devices in a customer power distribution network.
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Contents lists available at SciVerse ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
The frequency-independent control method for distributed generation systems Siamak Naderi a, Edris Pouresmaeil b,⇑, Wenzhong David Gao c a
Faculty of Azad University, Isfahan, Iran Centre d’Innovació Tecnológica en Convertidors Estátics i Accionaments (CITCEA-UPC), Departament d’Enginyeria Eléctrica, Universitat Politècnica de Catalunya, ETS d’Enginyeria Industrial de Barcelona, Barcelona, Spain c Department of Electrical and Computer Engineering, University of Denver, Denver, CO, USA b
a r t i c l e
i n f o
Article history: Received 6 July 2011 Received in revised form 27 August 2011 Accepted 18 September 2011 Available online 3 November 2011 Keywords: Distributed energy resources Distributed generation Hysteresis current control Reactive power compensation Rotating synchronous reference frame Voltage source inverter
a b s t r a c t In this paper a novel frequency-independent control method suitable for distributed generation (DG) is presented. This strategy is derived based on the abc/ab transformation and abc/dq transformation of the ac system variables. The active and reactive currents injected by the DG are controlled in the synchronously rotating orthogonal dq reference frame. The transformed variables are used in control of the voltage source inverter that connects DG to distribution network. Due to importance of distributed resources in modern power systems, development of new, practical, cost-effective and simple control strategies is obligatory. The new control method of this paper does not need a Phase Locked Loop (PLL) in control circuit and has fast dynamic response in providing active and reactive power to nonlinear load. From extensive simulation results, high performance of this control strategy in DG application is demonstrated with improved voltage profile, increased power factor and reduced total harmonic distortion. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Nowadays, energy technologies have a central role in social and economic development at all scales, from household and community to regional, national and international. Among its welfare effects, energy is closely linked to environmental pollution and degradation, economic development and quality of living [1]. Today, we are mostly dependent on nonrenewable fossil fuels that have been and will continue to be a major cause of pollution and climate change. The necessity of producing more energy combined with the interest in clean technologies yields in an increased development of power distribution systems using DG resources based on renewable energy sources. DG technologies include photovoltaic, wind turbines, fuel cells, small sized micro turbine packages, stirling-engine based generators and internal combustion engine-generators. These technologies are entering a period of rapid expansion and commercialization [2]. Perhaps the greatest challenge in realizing a DG future is to develop this technology for integration and control of renewable energy sources in smart grid distributed generation [3]. The smart power grid distributed energy system would provide the platform for the use of renewable sources and adequate emergency power for major metropolitan load centers and would safeguard in preventing the complete blackout of the interconnected power systems due to man-made events and environmental calamity and would provide the ability to break up the interconnected ⇑ Corresponding author. Tel.: +34 93 401 67 27; fax: +34 93 401 74 33. E-mail addresses: [email protected] (E. Pouresmaeil), Wenzhong. [email protected] (W.D. Gao). 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.09.034
power systems into smaller cluster regions [4,5]. As a result, a new simple low cost and practical control method is necessary for interconnection of DG resources to the distribution grid [6,7]. Several control techniques and strategies have been proposed and reported for interconnection of DG resources to the grid. In Ref. [8] an overview of control and grid synchronization algorithms, and their role and influence in the control of a DG system on normal and faulty grid condition were discussed. Different hardware structures like dq and stationary and natural frame control structures were presented and their major characteristics were pointed out. A discussion about different controllers for the grid-side converters, and their ability to compensate for low-order harmonics presented in the utility grid was given and four different control methods that a DG system can use during an unbalanced grid fault were discussed. In Ref. [9], a nonlinear control technique is proposed to enhance the dynamic performance of shunt active power filter which is modeled in the dq frame. NPC voltage source inverter (VSI) is proposed as the interfacing system of DG resources and AC grid. The exact feedback linearization theory is applied in the design of the controller. This control strategy allows the decoupling of the currents and enhances their tracking behavior and improves the DC-voltage regulation. In Ref. [10], a dual inverter is proposed for connection of wind energy to the grid. One of the two inverters in the dual inverter is connected to the rectified output of the wind generator while the other is directly connected to a battery energy storage system. This approach eliminates the need for an additional dc–dc converter and thus reduces power losses, cost and complexity. The main issue with this method is uncorrelated dynamic
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changes in dc-link voltages that results in unevenly distributed space vectors. Several other control strategies for interfacing system between different types of supplies based on renewable and non-renewable energy resources and electrical networks are proposed and presented for different objectives [11,12]. In all the proposed methods, a solution has been proposed for an important problem in electrical networks. This paper presents the theoretical development of a multi-objective control technique of VSI which considers different aspects of electrical network during integration of DG resources to the electrical grid. DG system can be connected to the network in series or shunt type. Shunt connection injects current at Point of Common Coupling (PCC), while series connection injects a voltage between the utility supply and the customer load. Because the compensated quantities (reactive power or harmonics) are related to the current, shunt type is more realistic as it injects current at PCC [3,13]. Fig. 1 shows the shunt connection of a DG system to the distribution network. Current controlled voltage source inverter (VSI) is proposed for interfacing between DG and distribution networks, because of its fast dynamic response, accurate performance, ease of implementation and its inherent closed loop control for the current to guarantee the required operating point [14,15]. The command signal for the VSI which is current signal in nature will include the information of active power supplied from DG system and reactive power required to compensate the voltage fluctuation at load-side PCC or total reactive power compensation and also harmonic currents. When interfaced to the grid with the auxiliary help of a battery to supply the transient need of power, the details on the distributed source behavior tend to lose importance when looking at the performance of the unit as seen from the grid terminals. Indeed, the VSI will be connected to the terminals of the battery and will only see a relatively stiff DC voltage. The power source no longer has a dramatically fast transient response, since its only task is to keep the battery charged. So, in this paper we look at the DG system as an inverter connected to a battery. This simplification makes the design and analysis of the power electronic interface less burdensome. The performance of the proposed system is simulated using Matlab/Simulink. The results are discussed to demonstrate the potential of the proposed technique.
1.1. Frequency independent control technique The current control techniques of VSI presented in this paper is based on analysis of voltage and current vector components mainly in a special reference frame with mathematical equations and transformation matrices [16]. To decompose voltage and current components in a rotating reference frame, calculation of instantaneous angle of voltage or current is needed. To obtain this angle,
VS
RS
LS i s
PCC
ic
il
Phase-Locked Loop (PLL) is commonly used in voltage source inverter’s control loop [17–19]. Employing of phase locked loop has some disadvantages such as problems due to synchronization of DG with the grid and elimination of a wide range of frequencies which is not favorable in DG’s application as an active power filter. In addition, PLL is very sensitive to noises and disturbances [20]. In frequency-independent control algorithm instantaneous angle of load voltage is calculated directly by decomposing voltage vector components in a rotating reference frame. Removing PLL from control circuit of voltage source inverter introduces a new control method for DG systems. In this control strategy synchronization problems will be resolved and dynamic response of DG will be improved. This control technique can: provide load active power, compensate load reactive power and track rapid variations in load reactive power, supply load harmonic currents. In consequence of these characteristics, DG can also compensate load voltage sags. 1.2. Voltage and currents in rotating and stationary reference frame, calculation of reference current of DG control system Voltages and currents of nonlinear DG link are shown in Fig. 2. To achieve frequency-independent control, voltage and current components are obtained in a stationary reference frame, i.e., in ab components by the following equation: !
v ¼ TV!and
!
i! ¼ TI
ð1Þ
where v , T, V, i and I are defined as:
2 3 rffiffiffi va 2 1 1=2 1=2 6 7 pffiffiffi pffiffiffi ; V ¼ 4 v b 5; v ¼ avb ¼ 3 0 3=2 3=2 vc 2 3 ila ! ia 6 7 i ¼ and I ¼ 4 ilb 5: ib ilc !
!
va T¼ vb
It is noted, in the three-wire systems with balanced load zero sequence component of voltage is null and therefore zero sequence current component is also null. In the next stage, injected current components of DG system to the grid must be calculated in ab frame. For this purpose, ab frame is transformed to synchronously rotating reference frame, i.e., in dq components. In this transformation d-axis vector is in direction of voltage vector. With this consideration, vertical component of voltage (q-component of Vs
Rs
Ls
is
SW
PCC
il
Utility Load
Current Filter
Load
ic
il
T T
VSI
vab,vbc
ic
VSI & Current Controller
C
DC/AC
vdc
ic*
DG Source Fig. 1. Shunt connection of a DG system to the grid.
Reference Generator Fig. 2. Voltage and current of nonlinear link.
DG
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Pref is the power that DG system must provide in fundamental fre quency. icd h1 is the d-component of DG link reference current in fundamental frequency. Due to limited output power of voltage source inverter, reference current must be restricted. Calculation of d-component of reference current with this method makes it possible to control maximum active power delivered to the grid by changing Pref. Pref depends on DG system capacity, capacity of power electronic devices and transformers. 1.3. Calculation of harmonic components of d-axis reference current Calculation of load current in dq reference frame by 5 makes it possible to separate fundamental and harmonic currents. ild can be separated into DC and alternative components as:
ild ¼ ild þIld
ð9Þ
Fig. 3. Voltage and current components in stationary and rotating synchronous reference frame.
voltage) in rotating synchronous reference frame is always zero (vq = 0) [3]. Fig. 3 shows the voltage and current components in stationary and rotating synchronous reference frames. Transformation matrix which is based on Park’s equations is given in the following equation:
ild ilq
¼
Cosh
Sinh
Sinh Cosh
ila
ilb
ð2Þ
where ild and ilq are direct and quadrature components of current in rotating synchronous reference frame respectively; h is instantaneous angle of load voltage. By Fig. 3, h can be calculated as:
h ¼ tan1
vb : va
ð3Þ
According to Fig. 3, d-component of voltage in stationary and rotating synchronous reference frame can be calculated as: !
!
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
v d ¼ j v dq j ¼ j v ab j ¼ v 2a þ v 2b :
ð4Þ
By (2)–(4) can be rewritten as [21]:
ild
ilq
¼
1
vd
v a v b ila v b v a ilb
ð5Þ
By 5, d and q-components of current in rotating synchronous reference frame can be calculated by means of current components in stationary reference frame. In rotating reference synchronous frame, quadrature component of load current is perpendicular to direct component of voltage (vd\ilq). So q-component of load current indicates required reactive power of the load. To compensate load reactive power, DG must provide a current with q-component equal to ilq. For this purpose, it is sufficient to set q-component of reference current of DG equal to q-component of the load current as shown in the following equation:
icq ¼ ilq
ð6Þ
ild is alternative d-component of load current in rotating synchronous reference frame which is related to harmonic components of load current and Ild is the DC term of load current in this frame which is related to fundamental frequency of load current. To compensate harmonic current it is necessary to separate alternative and constant components. For this purpose, a high pass filter must be used. To minimize the influence of the HPF’s phase responses, by means of a low-pass filter (LPF), a minimal phase HPF (MPHPF) can be obtained, the transfer function of this LPF has order and cutoff frequency as the same as HPF. So, the minimal phase HPF can be obtained simply by the difference between the input signal and the filtered one, which is equivalent to performing: HMPHPF(s) = 1–HLPF(s). A double-precision filter using the Chebyshev type-II fifth order low-pass filter is used for this purpose. Fig. 4 depicts amplitude and phase of high pass filter and minimum phase high pass filter. The filter considered has a cut-off frequency fc ¼ 2f (f = 50 Hz) which promises the extraction of DC components in the nonlinear load currents. So, harmonic components of load current at d-axis are obtained. To use distributed generation as active filter, harmonic components of load current must be supplied by DG. For this purpose, vertical component of nonlinear link reference current is obtained by 6 and DC component of reference current is calculated from:
where is calculated by 8. Equivalent reference currents in stationary reference frame are obtained by:
"
ica
¼
Pref
vd
vd
va vb
v b
"
icd
va
icq
# ð11Þ
:
2
ic
3 " # ica ica 6 7 ¼ 4 icb 5 ¼ T1 : icb icc
ð12Þ
For implementation, 1 can be rewritten based on line voltage
v¼
pffiffiffiffiffiffiffiffi 1 1=2 v ab pffiffiffi : 2=3 0 3=2 v bc
ð13Þ
By substituting 1 in 2 and considering ilc = (ila + ilb):
ild ilq
ð8Þ
1
By 1 and calculating inverse matrix, reference current in abc frame are achieved as:
!
icd h1
¼
P ¼ v d :icd
ponent of DG Link current. d-component of DG link reference current to provide active current in fundamental frequency can be calculate by 7. So we have:
#
icb
as:
vd is load voltage in fundamental frequency at the PCC icd is d-com-
ð10Þ
h1
icd h1
icq is the vertical component of DG link reference current that is shown in Fig. 2. By this consideration, total load reactive current is compensated. The active power injected from DG system to the grid is:
ð7Þ
icd ¼ ild þicd
¼
pffiffiffi Sinðh þ p=3Þ SinðhÞ ila 2 : Cosðh þ p=3Þ CosðhÞ ilb
So, by 12, 14 and icc ¼ ðica þ icb Þ:
ð14Þ
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Phase (degree)
Magnitude (dB)
0
MPHPF
-50
HPF
-100 -150 360 315 270 225 180 135 90 45 0 -45 0 10
HPF
MPHPF 1
2
10
10
3
10
Fig. 4. Amplitude and phase of high pass filter and minimal phase high pass filter.
"
ica
icb
# ¼
pffiffiffiffiffiffiffiffi 2=3
CosðhÞ
SinðhÞ
Cosðh þ p=3Þ Sinðh þ p=3Þ
"
icd
icq
# ð15Þ
h is calculated from 3. Eqs. 14 and 15 indicate Park transformation and its inverse respectively. Separation of current components into alternative and DC terms provide proper currents for voltage source inverter, introducing a flexible distributed generation with following characteristics: Compensation of harmonic currents (active filter). Compensation of harmonic currents and load reactive power (active filter and distributed static compensator). Compensation of harmonic currents and load reactive power and providing active power (DG system).
Fig. 5 shows the diagram of DG control system for harmonic compensation, reactive power compensation and active power control. 1.4. Current controller of voltage source inverter Many current control methods for three phase systems are presented in [22]. Among them, current control using hysteresis regulators are widely used. Some of the advantages of hysteresis current control (HCC) are: simplicity in implementation, high speed of current loop, independency from load parameters.
Fig. 5. Diagram of DG control system for harmonic compensation, reactive power compensation and active power control.
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2. Simulation results To describe and validate proposed control method, simulations are carried out for a distribution network connected with a nonlinear DG link in Matlab/Simulink environment. Its single-line diagram and principle of proposed control system are shown in Figs. 1 and 5 respectively. Simulation parameters are given in Table 1. It is considered that for the whole period of simulations a full-wave thyristor converter is fed by the main source. During simulation process active power which is delivered from DG link is considered constant. This assumption makes it possible to evaluate the capability of DG link to track the fast change in the reactive power, independently. To simulate a real distribution network, the loads are connected and disconnected to distribution network randomly
Fig. 6. Hysteresis current control (a) closed loop control and (b) switching technique demonstration.
Fig. 6 demonstrates the basic control algorithm of the current controlled VSI. HCC in nature is a closed loop control for the current of VSI. Comparison of the calculated reference currents and the actual DG injection currents generated by the VSI will result in the error signal (e in Fig. 6a), which controls the switches of the inverter. When the error reaches the upper limit of the hysteresis comparator, IGBTs (Insulated Gate Bipolar Transistor) are switched ON to increase the current; and when the error reaches the lower limit, the current is forced to decrease by switching the IGBTs OFF, Fig. 6b. These operations lead to the fast dynamic response that characterizes HCC among other current control techniques. The range of the error signal, h, directly controls the amount of ripples of the output current from the VSI and is called the hysteresis band. The current is forced to stay within these limits even while the reference current is changing. The switching frequency is altered by the width of the hysteresis band, the size of the inductor that the current flows through (Lc in Fig. 6) and the DC voltage (vdc) applied from the DG to the VSI. A practical method to calculate inductor value for current filter in nonlinear link is presented in [23]. According to this method, filter inductor is calculated by:
Lc ¼
2v dc 9hfsw:max
ð16Þ
where vdc is DC bus voltage, h is the hysteresis band, fsw.max is maximum switching frequency. From 16, maximum switching frequency can be calculated. This frequency is related to DC bus voltage and inversely related to hysteresis bands and filter inductor. By increasing switching frequency, output current ripple and the distortion of voltage and current at PCC are decreased. On the other hand, by increasing switching frequency, electro-magnetic interference and switching losses occur and high speed converters and comparators are needed.
Fig. 7. (a) Load current, nonlinear link current and source current before and after DG connection and before and after additional load connection and (b) d and qcomponents of load.
Table 1 Specification parameters. Vs (rms)
fs (Hz)
Rs (X)
Ls (H)
Rc (X)
Lc (H)
vdc (V)
h
Pload (kW)
Qload (kvar)
380
50
0.05
0.001
0.1
0.04
1000
±1
9
6
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and Total Harmonic Distortion (THD) of current waveform are calculated and compared with each other in various conditions. Since the principle of proposed current control technique is based on separating active and reactive current components in rotating synchronous reference frame (dq components), in all conditions d and q-component of load current are shown. To demonstrate the ability of nonlinear DG link to compensate whole reactive power, load voltage, load current and source current are shown in one figure simultaneously. The following subsections present the process of simulation for connection and disconnection of different kind of loads. 2.1. Connection of DG link to the distribution network and harmonic load increment The nonlinear DG link is connected to the network at t = 0.05 s. This process is continued until t = 0.15; at this moment another full-wave thyristor converter similar to the prior load is added to PCC and it is removed at t = 0.3 s. Figs. 7–9 shows the related currents, load voltage and current spectra, respectively. After connection of DG link the source current becomes zero and all the active and reactive current component including fundamental and harmonics frequency are provided by DG link, as shown in Fig. 7a. Reference currents during period of connection of DG link to the network are shown in Fig. 7b. The load current is fed from nonlinear link continuously until connection of additional load to the network. As shown in Fig. 8a, after connection of additional load, production in control circuit of DG system is delayed for one cycle. This is due to settling time of MPHPF filter. After the transient times, the load voltage and source current are in phase and source does not need to provide reactive and harmonic currents for the load which
Fig. 9. Currents spectra. (a) Load current spectra before connection of DG link to the network. (b) Load current spectra after connection of additional load and (c) Source current spectra after connection of additional load.
is shown for phase a. With the same delay as before, additional load is removed at t = 0.3 s. After the pass of the transient times the source current becomes zero. As shown in Fig. 8, load harmonic currents are provided by DG and source current is sinusoidal but there are sharp edges on current waveforms which are related to high order harmonic frequencies and created during switching of thyristor converters. To evaluate the capabilities of DG link to compensate harmonic currents, the spectra of currents before and after connection of DG link and after connection of additional load are shown in Fig. 9. Fig. 9a shows that before connection of additional load the THD is 21.8%. After connection of additional load this value is 21.91%, as Fig. 9b indicates. Fig. 9c shows that the THD of source current after connection of additional load is just 5.86%. The comparison between this information demonstrates capabilities of DG link to compensate harmonic currents of the load. 2.2. Linear load increment Fig. 8. Source current, load voltage and load current (a) before and after connection of additional load and (b) before and after disconnection of additional load.
In this section, to evaluate DG link to track both harmonic and sinusoidal currents the RL load is connected to PCC at t = 0.4 s
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and it is removed at t = 0.55 s. The related simulation results are shown in Figs. 10–13. Additional load is a resistive-inductive load. Maximum delivered power from DG system is considered constant (Pref = 8 kW). Considering that all required reactive power of additional load is provided by DG system, additional required load active power must be provided by main source. Fig. 10a shows load current, source current and nonlinear link current during load increment. At t = 0.4 s, an extra load is connected to the distribution network and due to delay settling time of MPHPF filter, production in DG link circuit is started 0.02 s after load connection. According to Fig. 10a, load harmonic current is provided by DG and source current is sinusoidal. The reference currents in dq frame, which are equal to d and q-components of the load current, are shown in Fig. 10b. The step response of the MPHPF which causes the delay in the control circuit of DG link is apparent from this shape. After production in DG link control circuit, load voltage and source current become in phase which is shown for phase a in Fig. 11a. So, source does not provide reactive components. The
Fig. 11. Source current, load voltage and load current (a) before and after connection of additional RL load and (b) before and after disconnection of additional RL load.
Fig. 10. (a) Load current, nonlinear link current and source current before and after additional RL Load connection and disconnection and (b) d- and q- components of load.
Fig. 12. Currents spectra after connection of additional RL load. (a) Load current spectra and (b) source current spectra.
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Fig. 14. Source, load and DG link (a) active power and (b) reactive power.
Fig. 13. (a) Load current, nonlinear link current and source current before and after disconnection of additional RL load and (b) d and q-components of load.
additional RL load is removed at t = 0.55 s. As shown in Fig. 11b, after the pass of the transient times the source current become zero. Fig. 12a shows the THD after connection of additional RL load to the distribution network is 10.89%. Fig. 12b shows that the source current THD in this period is just 2.91% which illustrates the potential of DG link to compensate considerable amount of harmonic frequencies. After disconnection of additional RL load at t = 0.55 s, as shown in Fig. 13, the load, DG link and source currents return to their prior values. It is noted that all voltage and current waveforms vary within the hysteresis band. Finally, the active and reactive powers which pass through network are shown in Fig. 14. Fig. 14a shows source, load and DG link active power during connection of DG link and connection and disconnection of extra loads. As one can predict, the waveform of active power of DG link contains a step response which is related to MPHPF. So, the delay and swings in this wave are due to the same reasons mentioned above. In addition, after connection of DG to the network the active power which is delivered from source is decreased to zero and DG link delivered active power, completely tracking load active power. Due to delay settling time of MPHPF, after connection of additional
load at t = 0.15 s, some swings appear in active power waveform. The transient time takes one cycle (0.02 s). The rate of changes in active power of DG has fast slope at t = 0.05 s. That is due to, before connection of distributed generation link, the DG control circuit has some information about the nature of load. Fig. 14b indicates source, load and DG link reactive power. As there is no filter in the control loop of q-component of DG link reference current, the waveform of DG reactive power has better response than DG’s active power response. This Figure also shows the capability of DG system to track and compensate load reactive power, completely. This can prevent load voltage fluctuations in case of sudden change in load reactive power. 3. Conclusions In this paper, a frequency-independent control technique for distributed generation resources has been presented. Due to sensitivity of PLL to noises and distortion, its elimination can bring benefits for robust control against distortions in DG applications. Also, the problems due to synchronization between DG and network do not exist and DG link can be connected to the distribution network without any current overshoot. One other advantage of proposed control method is its fast dynamic response in tracking reactive power variations; the control loops of active and reactive power are considered independent. By the use of proposed control method, DG system is introduced as a new alternative for distributed static compensator in distribution network. Simulation results illustrate that in all conditions the load voltage and source current are in phase and so, by improvement of power factor at PCC, DG systems can act as power factor corrector devices. The simulation results indicate that proposed DG system can provide required harmonic load currents in all situations. So, by reducing THD of source current it can act as an active filter. The proposed control method can be used for different types of DG resources as power quality improvement devices in a customer power distribution network.
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