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Intertied hybrid power system comprises of multifrequency, multivoltage individual hybrid power system (HPS). The benefit of intertied HPS includes reduced reserve capacity, improved voltage & frequency regulation, and flexibility in operating voltage & frequency. These benefits can be attained by a suitably designed power management scheme. There are many methods available to manage the power in standalone intertied HPS, out of them conventional droop control is simple and popular method, although it has limitations in terms of overlooking system capacity and deviation of voltage & frequency with sudden impact of loads. This necessitates an adaptive power sharing method which should cope with the coordinated deviation in voltage and frequency. Therefore coordinated droop control for multifrequency, multivoltage intertied HPS is proposed in this work. In proposed control scheme a correction factor with respect to system capacity and critical load capacity is integrated to achieve coordinated deviation in voltage and frequency which conquer the limitations of conventional method.
intertied hybrid power system, droop control, interlinking power converter, coordinated control, adaptive power sharing
Hybrid power system (HPS) comprises of various energy sources (conventional & renewable) like PV, fuel cells, wind generators, diesel generators and various storage technologies like batteries, flywheels and ultracapacitors [1]. Hybrid power system is better means of utilization of renewable energy and diminishing the environmental hazard of fossil fuels. A few applications of hybrid power systems are observed in the industrial, institutional, navy, marine, aerospace, and remote area etc. There are many research possibilities in hybrid power systems with intention to strengthen the system capacity and enhancement in the efficiency and reliability. As majority of utility grids are still operating on AC system, AC HPS are more popular however renewable sources with DC output emerged the concept of DC HPS. A hybrid power system has benefits of optimum use of available resources, improved stability, reliability, though the hybrid power system has limitations to supply either AC or DC load depending on the source. These limitations are overcome by intertied hybrid power system which is formed by interlinking of different types of hybrid power systems compatible with both AC and DC technologies. AC and DC HPS can be operated independently, but for more reliability and security they are intertied by interlinking power converters. Intertied HPS by interlinking power converters for ACDC HPS has been successfully investigated [26]. These intertied HPS can support selfsustaining military base, hospitals, industrial plants, or institutions where power outage is not permissible. The intertied HPS may also be designed with own preferred frequency, voltage and network arrangement to meet the load demand. It is essential to manage the power in the intertied HPS through a controller for better power sharing, stable operation and high efficiency [7]. The intertied HPS is a focus of research due to its high reliability and flexibility with integration of renewable energy sources.
Research on intertied HPS has grown progressively but mainly confined to single frequency and single voltage ACDC HPS [8]. Consequently, interlinking of multiple frequency AC HPS and multiple voltage DC HPS merges the profits of each HPS. An intertied hybrid power system can better share active and reactive powers among its entities by selecting different frequencies and voltages in individual HPS for improved performance and supply reliability. Intertied HPS are working as autonomous system with their own preferred voltage and frequencies. A physical dual frequency system of 50 Hz and 60 Hz interlinked by interlinking power converter has been built for Ross Island Antarctica Project (Dual frequency) [9]. These systems have the advantages of enhanced reliability, security and efficiency with optimal use of energy resources. This dragged the attention of researchers in the area of intertied HPS in last few years.
Also, research shows that the multifrequency AC HPS and multivoltage DC HPS comprising of different ACDC HPS operating at their rated voltages and frequencies will be able to reduce transmission and distribution losses, which create interest of researchers in intertied HPS. Having different voltage and frequency introduces more flexibility into the system, and intertying with other HPS requires the insertion of interlinking power converters. Control of standalone hybrid power system is complex but has wide applications in remote areas [1012]. The main control variables of an intertied hybrid power system are voltage, frequency, active and reactive power. The design of power sharing controller is a major challenge due to the variation in operating frequency and voltage of AC & DC HPS. Since the considered system is in standalone mode the control strategy is complex and should maintain the common DC bus voltage with adaptive power sharing and limited deviation in AC HPS frequency and DC HPS voltage under varying load conditions. There are many control techniques for intertied HPS has been already proposed in literature. In centralized control, the need for fast communication link and single point failure decreases the reliability which realized the need of decentralized controllers for power sharing where droop control methods are more popular. Various droop control methods have been proposed in the literature for AC and DC HPS which offers simplicity and better performance. Various droop control methods like conventional droop [1316], voltagereal power droop (VPD) [17], frequencyreactive power boost droop (FQB) [17, 18], QV droop [19], angle droop [19], virtual frame transformation [20], virtual impedance method [21], integral droop [22], adaptive droop [23] etc. are already in existence. Conventional droop control is a popular method to manage the power in standalone mode of intertied HPS due to its simplicity. However limitations of conventional droop in terms of influenced by system parameters, poor voltage regulation, bandwidth variation of active and reactive power controllers affects the voltage and frequency control motivated to work in the area of specific droop control for intertied HPS. Intertied hybrid power systems with same or different voltage or frequency has the advantages like fulfillment of power demand, enhanced reliability, security and efficiency with optimum use of resources [24, 25]. Controlling of multiple voltages and multiple frequencies in intertied HPS is challenging task [26]. Power quality issues with multiple power electronic interfaces in intertied HPS are another major concern [27, 28]. Another challenge with intertied hybrid power system is appropriate power sharing with coordinated deviation in voltage and frequency for sudden load change in consideration to system capacity has to be addressed by autonomous control without communication link [2932]. In this context proper controller with power management strategy is required which should cope with the deviation with voltage and frequency in comparison to existing control [3337].
In perspective of the literature survey following research gaps have been identified.
(1) Autonomous control for multifrequency and multivoltage intertied HPS is missing.
(2) Improved power sharing within the intertied HPS with coordinated deviation in voltage & frequency and flexibility in selection of voltage & frequency for HPS along with consideration of system capacity is missing.
(3) Multifrequency control and multivoltage control should incorporate corrections obtained from coordinated control to consider system capacity.
To overcome above mentioned issues control power sharing in multifrequency and multivoltage intertied HPS normal droop techniques cannot be feasible. So there is requirement of specific droop technique which assures better voltage regulation and accurate power sharing among sources. This task can be fulfilled only when the control technique considers the system capacity and critical load so that accurate power sharing is assured among each HPS and loads [3337].
Following contributions have been presented by author in this paper.
(1) Coordinated multivoltage, multifrequency droop control is a better choice in which by including correction factor in terms of system capacity and critical load, better performance of the system can be achieved.
(2) To get the correction factor including system capacity, coordinated control among individual HPS is preferred which ensures power fluctuations to be divided in all HPSs.
(3) Proposed power sharing controller for intertied HPS should be capable of handling the power management, coordinated deviation in voltage & frequency and flexibility in selection of voltage & frequency for HPS along with consideration of system capacity.
The structure of this paper is organized as follows: Section2 presents coordinated control, Section3 presents adaptive multifrequency control and Section4 discuses adaptive multivoltage control, performance evaluation of proposed control strategy is analyzed in Section5 and Section6 presents conclusion.
In perspective of the control structure, power interaction among different HPS in a standalone intertied system is more complicated. Since power fluctuations result in the change in the output of system; coordinated control among individual HPS ensures power sharing among different HPS. Since in all HPS, droop controlled strategy is preferred; thereby AC frequency and DC voltage vary according to change in load demand. Here both AC and DC HPS are connected to common bus. To maintain the proper power sharing among different HPS necessitates coordinated control strategy. The objective of coordinated combined ACDC droop based adaptive controller is to share appropriate active power in intertied HPS with coordinated voltage and frequency deviation under varying load conditions. The proposed control technique is designed with adaptive correction factors δv and δf for combined ACDC droop. The control law for adaptive correction factors for p no. of AC HPS and q no. of DC HPS can be expressed as
$\delta f_{p}=\left(k_{p, p}+\frac{k_{i, p}}{s}\right)\left[\frac{\left(v_{c b}v_{c b}^{*}\right)}{v_{c b}^{\max }v_{c b}^{\min }}\alpha_{p} \frac{f_{p}f_{p}^{*}}{f_{p}^{\max }f_{p}^{\min }}\right]$ (1)
$\delta v_{q}=\left(k_{p, q}+\frac{k_{i, q}}{s}\right)\left[\frac{\left(v_{c b}v_{c b}^{*}\right)}{v_{c b}^{\max }v_{c b}^{\min }}\alpha_{q} \frac{v_{d c, q}v_{d c ., q}^{*}}{v_{d ., q}^{\max }v_{d c, q}^{\min }}\right]$ (2)
Here δf_{p} and δv_{q} are the coordinated control signal for IPC of p^{th}AC HPS and q^{th} DC HPS respectively. AC and DC HPS, PI parameters are k_{p} and k_{i}. α_{p} and α_{q} are the correction coefficients in consideration to capacity of p^{th} AC and q^{th} DC HPS respectively. Here f and v_{cb} denotes frequency and common bus voltage with superscript *, max, min are used for rated values, maximum and minimum values respectively. By considering the capacity of the system, it is easier to support weak HPS by strong HPS. The proposed correction coefficient of p^{th} HPS is represented as
$\alpha_{p}=\left(\frac{H_{p}^{\text {total}}}{H^{\text {total}}}\right)^{1} \frac{H_{p}^{c}}{H_{p}^{\text {total}}}$ (3)
Figure 1. Corrections for coordinated power control
where, H_{p}^{total} and H_{p}^{c} are total and critical load capacity of p^{th} HPS and H^{total} is the total capacity of intertied HPS. The value α_{p} is large for small capacity of HPS with high amount of critical load connected, resulting in small deviation in DC voltage and AC frequency. Also, synchronization with change in voltage and frequency proves the efficacy of the proposed control technique. In coordinated operation ac frequencies and dc voltages decrease or increase at the same time. This results in synchronized changes in AC and DC HPS power. Under steady state condition, the relation between voltage and frequency considering capacity of the system is given by
$\frac{v_{c b}v_{c b}^{*}}{v_{c b}^{\max }v_{c b}^{\min }}=\alpha_{p} \frac{f_{p}f_{p}^{*}}{f_{p}^{\max }f_{p}^{\min }}=\alpha_{q} \frac{v_{d c, q}v_{d c, q}^{*}}{v_{d c, q}^{\max }v_{d c, q}^{\min }}$ (4)
Figure 1 shows the corrected relative changes in AC frequency and DC voltage for proposed control algorithm. The operating points on AC and DC droop are the basis of active power sharing. The feedback variables positioned at IPCs to share the coordinated power can be realized to improve the reliability of the system.
This method is proposed to connect two AC HPS of frequency 50Hz and 60Hz. The multifrequency system is shown in Figure 2, where an interlinking power converter is responsible for bidirectional power flow between two HPS of different frequency. As the intertied HPS considered is in standalone mode so the increase/decrease in demand causes deviation in frequency. This frequency deviation needs attention as it may causes failure of devices. So in order to protect the whole system controllers have to be designed in such a way that it should not cause more deviation in frequency with sudden impact of increase/decrease in load.
Figure 2. Multi frequency system configuration
Figure 3. Control circuit for single and multifrequency control
Figure 4. Multifrequency droop and normalized frequency characteristics of HPS_{1}, and HPS_{2}
IPC_{1} regulates DC link voltage while IPC_{2} regulates the frequency of HPS_{1} and HPS_{2}. The outputs of current control loop u_{d1} and u_{q1} can be represented as:
$u_{d 1}=v_{d 1}i_{q 1} \omega_{1} L_{1}+k_{p}\left(i_{d 1}^{r e f}i_{d 1}\right)+k_{i} \int\left(i_{d 1}^{r e f}i_{d 1}\right) d t$ (5)
$u_{q 1}=v_{q 1}i_{d 1} \omega_{1} L_{1}+k_{p}\left(i_{q 1}^{r e f}i_{q 1}\right)+k_{i} \int\left(i_{q_{1}}^{r e f}i_{q 1}\right) d t$ (6)
where, i_{d1}^{ref} and i_{d1 }are the reference and measured currents of HPS_{1}, respectively; $\omega_{1}$ is the angular frequency of HPS_{1, }k_{p} and k_{i}are the proportionalintegral (PI) parameters of current control loop. The DC link voltage controller generates reference current i_{d1}^{ref} as:
$i_{d 1}^{r e f}=k_{p d}\left(v_{d c}^{r e f}v_{d c}\right)+k_{i d} \int\left(v_{d c}^{r e f}v_{d c}\right) d t$ (7)
$i_{q 1}^{r e f}=k_{p q}\left(Q_{a c1}^{r e f}Q_{1}\right)+k_{i q} \int\left(Q_{a c1}^{r e f}Q_{1}\right) d t$ (8)
where, v^{ref}_{dc} and v_{dc} are the reference and measured dcvoltages of the interlinking power converter, respectively; k_{pq}, k_{iq} and k_{pd}, k_{id} are the PI parameters of the voltage controller and DClink voltage controller respectively, Q^{ref}_{ac_1}and Q_{1} are reference and measured reactive power. IPC_{2} has responsibility of multifrequency control which comprises of reactive power control loop, current control loop, and multifrequency control loop. Here i^{ref}_{d2} and i^{ref}_{q2} are the reference direct axis and quadrature axis current of HPS_{2}. The generation of reference currents, i^{ref}_{d2} and i^{ref}_{q2}, is through reference real and reactive power.
$i_{q 1}^{r e f}=\frac{\frac{2}{3}\left(v_{d 2} P_{I P C}+v_{q 2} Q_{a c2}^{r e f}\right)}{v_{d 2}^{2}+v_{q 2}^{2}}$ (9)
$i_{q 2}^{r e f}=\frac{\frac{2}{3}\left(v_{q 2} P_{I P C}v_{d 2} Q_{a c2}^{r e f}\right)}{v_{d 2}^{2}+v_{q 2}^{2}}$ (10)
The reference real power P_{IPC} is given by
$P_{I P C}=k_{p a c}\left(f_{1}^{\prime}f_{2}^{\prime}\right)+k_{i a c} \int\left(f_{1}^{\prime}f_{2}^{\prime}\right) d t$ (11)
The control strategy for multifrequency control is shown in Figure 3.
Power sharing among sources in an AC HPS can be accomplished through droop control method with δf as the change in the frequency obtained from Eq. (1) with change in load among different HPS obtained from coordinated control among different AC HPS. Here P_{acp} is the power output and P_{acp}^{max} is the maximum active power. Power sharing among p sources in AC HPS can be obtained as
$\frac{P_{a c1}}{P_{a c1}^{\max }}=\frac{P_{a c2}}{P_{a c2}^{\max }} \ldots \ldots \frac{P_{a cp}}{P_{a cp}^{\max }}$ (12)
The objective of coordinated droop based adaptive controller is to share appropriate active power in intertied HPS with coordinated frequency deviation under varying load conditions. Here f’_{1} and f’_{2} represent normalized frequencies of individual AC HPS_{1} and AC HPS_{2} respectively. P_{IPC} represents power flow through interlinking power converter. Here K_{pac} and K_{iac} are the proportional and integral control gain for the multi frequency control. Q^{ref}_{ac_2} represents reference reactive power of the HPS_{2}. The normalization of individual HPS frequency is done to achieve limited frequency deviation. Figure 4 shows the proposed droop control for AC HPS. Initially, the normal operation points of two HPS are represented as X_{1}and X_{2}. The sudden increase in load on HPS_{1} reduces HPS_{1} frequency from f_{10} to f_{11}. The operating point of HPS_{1} shifts from X_{1} to Y_{1}. To compensate the load disturbance in HPS_{1}, power from HPS_{2} is transferred to HPS_{1} through IPC. In order to accomplishment of this task, the adaptive controller senses the difference in the reference and the measured values of load power and generates the correction factor accordingly. This control action results in recovery of HPS_{1} frequency although HPS_{2} frequency decreases slightly. By proposed control, the frequencies of HPS_{1 }and HPS_{2} are achieving new steadystate values (Z_{1} and Z_{2}). Where, f_{1}represents the measured frequency of HPS_{1}, f^{*} is the rated frequency of HPS_{1}, f’_{1} is the normalized frequency of HPS_{1}.
The It is a challenging situation for flexible intertied HPS in standalone operation where the total load is to be shared and managed autonomously. The proposed scheme involves fast and flexible power control which minimizes the system dynamics. The adaptive control proposed includes coordinated control to share appropriate power among different HPS according to their ratings. The proposed control technique is designed with adaptive correction factors δv obtained from Eq. (2) for intertied HPS. Since power fluctuations result in change in the output of system; coordinated control among individual HPS ensures power sharing among different HPS. The objective of proposed controller is to share appropriate active power in intertied HPS with coordinated voltage deviation under varying load conditions. The proposed control technique is designed with adaptive correction factors δv. This method is proposed to connect q no. of DC HPS with common bus. For simplicity in this case two DC HPS of voltages 500V and 800V through a common DC bus of 1000V is considered as shown in Figure 5, where interlinking power converter (IPC) is responsible for bidirectional power flow between two HPS of different voltages.
DC sources are connected to DC bus through bidirectional converter. The function of IPC_{1} is to maintain the common bus voltage with bidirectional power flow. Bidirectional converter can be isolated or nonisolated. In nonisolated converter source and load does not have galvanic isolation while in isolated converter there is galvanic isolation by high frequency transformer. Due to simplicity of nonisolated converter it has been used in this work. The control strategy adopts droop control for power sharing among DC HPS. The control method for multivoltage control is shown in Figure 6.
Figure 5. Multivoltage control system configuration
Figure 6. Control circuit for multivoltage control
Power sharing through DCHPS droop control is simple where DC sources are controlled with one droop characteristic given by
$v_{d c}^{r e f}=\left(v_{d c}^{*}+\delta v_{q}\right)r_{q} i_{d c}$ (13)
Here the variables used as v_{dc}^{ref}, v_{dc}^{*}, r_{q}, i_{dc}, δv_{q} are reference output DC voltage, rated DC voltage, droop coefficient, actual output DC current, and coordinated control signal for IPC of q^{th} DC HPS. For different DC HPS v_{dc}^{* }can be different. Droop coefficient r_{q} and correction factor δv_{q}is given by
$r_{q}=\frac{V_{d c}^{\min }V_{d c}^{\max }}{P_{d cq}^{\max }}$ (14)
Figure 7 shows the droop characteristics of power sharing in multivoltage DC HPS with droop coefficient as r_{q} (i.e. r_{1} and r_{2}). Here the droop characteristics shown clearly mention the bidirectional power sharing of IPC in both modes (unidirectional and bidirectional).
Figure 7. Droop characteristics of multivoltage control of DC HPS
To analyze the performance of multifrequency and multivoltage intertied HPS two methods: conventional droop and adaptive coordinated droop have been proposed. Adaptive coordinated droop technique is designed with system capacity into consideration and then correction factor is employed to achieve better power sharing with reduced deviation in frequency and voltage. Proposed adaptive coordinated droop considers the load and system capacity and automatically calculates correction factor under varying load condition and makes the system adaptive. A comparative conventional droop control and adaptive coordinated droop control for multifrequency and multivoltage intertied HPS has been done. By analyzing the performance of the control schemes it has been observed that adaptive coordinated droop provides better power sharing and less deviation in frequency and voltage as compared to existing techniques. MATLAB/simulink environment has been used to prove the efficacy of proposed methods. Proposed control methods have been assessed on the basis of deviation in voltage and frequency. In adaptive coordinated droop control correction factor automatically changes with loading and integrated which makes the system adaptive and results in less deviation in voltage and frequency.
5.1 Performance evaluation of intertied HPS for multifrequency control
Frequency plays an important role in the system stability. If the frequency deviates from desired value there will be frequencypower imbalance and may result in power system collapse. Frequency deviation under the prescribed limit is necessary requirement for proper working of the system. The main aim of the proposed control is to get the deviation in frequency under the prescribed limit under load changing scenario. The test system comprises of two standalone HPS; HPS_{1} and HPS_{2} of frequency 60Hz and 50Hz respectively. The maximum frequency deviation of 1% is permissible. Various load change scenarios are considered in this case. HPS_{1} and HPS_{2} rated powers are taken as 80KW and 120KW respectively. The proposed controller dynamic performance is compared with the single frequency control method. In single frequency control, if one HPS is overloaded the frequency deviation will be observed in that HPS only while other HPS will have the constant frequency. This shows that the additional load applied to one HPS is not shared by the other. In multifrequency control, if one HPS is overloaded the other HPS is forced to share the load so that the deviation in frequency should be less. To verify the effectiveness of multifrequency control low overloading and heavy overloading conditions are analyzed. This can be observed by frequency deviation in both HPS at much reduced level. Two cases considered in this study are as follows:
5.1.1 CaseI: Low overloading on HPS_{2}
Figure 8 shows variation of load power with time where stateI represent rated state with HPS_{2} loading 120KW, in stateII load power of HPS_{2} changes from 120KW to 140KW and in stateIII load of HPS_{2} decreases from 140KW to 130KW while HPS_{1} is delivering 80KW in all states. In stateII and stateIII overloading of 16.7% and 8.3% occurred respectively. Initially system is working at normal frequency under rated load condition. In stateII and stateIII when 20KW and 10KW additional load is connected respectively at HPS_{2} causes reduction of the frequency in HPS_{2 }only by single frequency control while in multifrequency control deviation in frequency of HPS_{1} and HPS_{2} are shared according to system capacity.
Figure 8. Load power under caseI for singlefrequency and multifrequency control
Figure 9. Deviation in frequency of HPS_{1} and HPS_{2} under caseI for singlefrequency and multifrequency control
Figure 10. Load power under caseII for singlefrequency and multifrequency control
Figure 11. Frequency of HPS_{1} and HPS_{2} under caseII for singlefrequency control and multifrequency control
As observed from Figure 9, in stateII single frequency controller results in deviation of frequency for HPS_{2} by about 0.4 Hz while in multifrequency controller the deviation observed in HPS_{1} by 0.16 Hz and HPS_{2} by 0.24 Hz which is very small in comparison to single frequency controller. In stateIII single frequency controller results in deviation of frequency in HPS_{2} by 0.2 Hz while in multifrequency controller, deviation in frequency is observed as 0.08 Hz and 0.12 Hz respectively for HPS_{1} and HPS_{2}. The deviation in frequency in both the control is under the limit for low overloading condition however less deviation is observed in multifrequency control as compared to single frequency control.
Results of single frequency control shown in Figure 9 indicate that overloading of 20KW and 10KW on HPS_{2 }in stateII and stateIII respectively are not shared by HPS_{1}. That is why there is large frequency variation in HPS_{2} while there is no frequency variation in HPS_{1}. With the application of multifrequency control, the overloading of HPS_{2} is shared by HPS_{1} causing a slight frequency variation in HPS_{1 }(less than 1%) which is negligible. Also with the application of multifrequency control the frequency deviation in HPS_{2} is also reduced as compared to deviation in single frequency control. Here total overloading on HPS_{2} is 16.7% and 8.3% which is shared by HPS_{1} and HPS_{2} with 40% and 60% so that there will be lesser burden on both of the HPS and less frequency deviations are observed in both HPS. This makes the system more reliable especially in case of variation in load. It is clear that system response for load varying condition is improved with multifrequency controller as compared to single frequency controller.
5.1.2 CaseII: Heavy overloading on HPS_{2}
This case represents heavy overloading on HPS_{2} which causes system frequency to cross the threshold limit. In this case stateI is rated state with HPS_{2} rated loading 120KW, in stateII at 0.5sec 30KW additional load is connected on HPS_{2} and in stateIII at 1 sec 20KW additional load is connected at on HPS_{2}. HPS_{1} load is 80KW for all states. In stateII and stateIII overloading of 25% and 16.7% occurred respectively. Figure 10 represents variation of load power with time in caseII.
As HPS_{2} is heavily overloaded the frequency of HPS_{2} drops suddenly by 0.6Hz and 0.4Hz in stateII and stateIII respectively for single frequency controller which crosses threshold limit. To overcome the problem of over limit of frequency deviation in single frequency control load is shared in multifrequency controller so that the frequency deviations in stateII for HPS_{1} and HPS_{2} are 0.24Hz and 0.36Hz respectively while in stateIII frequency deviations for HPS_{1} and HPS_{2} are 0.16Hz and 0.24Hz respectively. Frequencies of the two HPS are regulated within the allowable deviation range for multifrequency control. The frequency deviations of both HPS with the disturbance of load in HPS_{2} for single and multifrequency control are shown in Figure 11.
Results of single frequency control shown in Figure 11 indicate that overloading of 30KW and 20KW on HPS_{2 }in stateII and stateIII respectively are not shared by HPS_{1} which results in large frequency variation of 0.6Hz in HPS_{2} (more than prescribed limit i.e. +0.5 Hz) while there is no frequency variation in HPS_{1}. With the application of multifrequency control the overloading of HPS_{2} is shared by HPS_{1} causing a slight frequency variation in HPS_{1 }(less than 1%) which is negligible. Also with the application of multifrequency control the frequency deviation in HPS_{2 }is also reduced as compared to deviation in single frequency control. Here total overloading is shared by HPS_{1} and HPS_{2} with 40% and 60% respectively so that there is not over burden on any of the HPS and less frequency deviations are observed in both HPS. This improves the system reliability particularly in case of variation in load and defines the suitability of method for multifrequency intertied HPS. The multifrequency control proposed for managing the frequencies of multifrequency intertied HPS is effective for power sharing among two HPS. A comparison study for frequency deviation with single frequency control and multiple frequency control for both cases has been presented in Table 1.
Table 2 shows the %overloading shared by both HPS under single frequency control and multifrequency control. It is clear from Table 1 and Table 2 that in caseII for t=0.5 sec. with single frequency control, frequency deviation is beyond threshold limit while multifrequency control results in less deviation by sharing overload on HPS_{1} and HPS_{2}. The multifrequency control strategy is suitable for intertied HPS due to the ability of bidirectional power sharing among two HPS. It is a simple approach which provides better power sharing without any communication link so offers reduced cost with no single point failure.
Table 1. Deviation of frequency in Hz for single and multifrequency control
Case 
Time (sec.) 
Single Frequency Control 
Multifrequency Control 

HPS_{1} 
HPS_{2} 
HPS_{1} 
HPS_{2} 

CaseI 
t=0.5 
0 
0.4 
0.16 
0.24 
t =1 
0 
0.2 
0.08 
0.12 

CaseII 
t =0.5 
0 
0.6 
0.24 
0.36 
t =1 
0 
0.4 
0.16 
0.24 
5.2 Performance evaluation of intertied HPS for multivoltage control
Voltage is an important controlling parameter in power system. Deviation in voltage beyond threshold can cause voltage fluctuations and in turn affect the appliances in house hold and industries. As all the equipments connected to grid are working at rated voltage, any variation in voltage affects the whole system. So it is desirable to get the deviation in voltage under the prescribed limit. The proposed multivoltage control is tested on multivoltage intertied HPS, which consists of two standalone DC HPS; HPS_{1} and HPS_{2} of voltage 500V and 800V respectively through interlinking power converter. The maximum voltage deviation allowed is +25V for HPS_{1} and +40V for HPS_{2}. DC HPS_{1} and DC HPS_{2} rated power are 65KW and 90KW respectively. Initial loading on HPS_{1} and HPS_{2} are 65KW and 90KW. The dynamic performance of the proposed multivoltage control is synthesized, with low and heavy overloading cases as follows:
5.2.1 CaseI: DC HPS_{2} low overloading
Figure 12 shows load power variations with time in caseI. In stateII and stateIII, 30KW and 20KW additional load is connected at HPS_{2} respectively with no variation in load on HPS_{1}. With conventional control the deviation in voltage of HPS_{2} are observed as 30V and 20V respectively for stateII and stateIII which is beyond prescribed limit. With overloading of 33.33% and 22.22% on HPS_{2} in stateII and stateIII respectively multivoltage controller shares additional loading among HPS_{1} and HPS_{2} in proportion to 42% and 58% respectively.
The multivoltage controller causes reduction in voltage on HPS_{1} by 12.58V and 8.39V in stateII and stateIII respectively while HPS_{2} voltage deviated by 17.52V and 11.61V in stateII and stateIII respectively. In multivoltage controller the voltage deviation in both the HPS are shared and under the allowable limit which results in good dynamic performance of the system. Figure 13 represents deviation in voltage for both HPS under conventional and multivoltage control.
Table 2. %overloading shared in single and multifrequency control
Case 
Time (sec.) 
Overloading 
Single Frequency Control 
MultiFrequency Control 

HPS_{1} 
HPS_{2} 
HPS_{1} 
HPS_{2} 
HPS_{1} 
HPS_{2} 

I 
t=0.5 
0KW (0%) 
20KW (16.7%) 
0KW (0%) 
20KW (100%) 
8KW (40%) 
12KW (60%) 
t =1 
0KW (0%) 
10KW (8.3%) 
0KW (0%) 
10KW (100%) 
4KW (40%) 
6KW (60%) 

II 
t =0.5 
0KW (0%) 
30KW (25%) 
0KW (0%) 
30KW (100%) 
12KW (40%) 
18KW (60%) 
t =1 
0KW (0%) 
20KW (16.7%) 
0KW (0%) 
20KW (100%) 
8KW (40%) 
12KW (60%) 
Figure 12. Load power under caseI for multivoltage control
Figure 13. DC voltage deviation of HPS_{1} and HPS_{2}, under caseI for conventional and multivoltage control
Figure 14. Load power for caseII under multivoltage control
Figure 15. DC voltage deviation of HPS_{1} and HPS_{2}, under caseII for conventional and multivoltage control
5.2.2 CaseI: DC HPS_{2} low overloading
This case represents heavy overloading condition on one HPS such that the voltage deviation is beyond threshold with conventional controller while multivoltage controller shares the overloading which results deviation in voltage under the prescribed limit. In this case stateI represent rated state with 90KW load, additional load of 45KW and 10KW is connected on HPS_{2} in stateII and stateIII respectively while HPS_{1} has constant load of 65KW. Figure 14 represents variation of load power in caseII.
As HPS_{2} is heavily overloaded in stateII, voltage deviation of HPS_{2} observed as 45V with conventional controller while in multivoltage controller the voltage deviations for HPS_{1} and HPS_{2} are 18.87V and 26.13V. In stateIII additional 10KW load results in voltage deviation on HPS_{2} as 10V while in multivoltage controller as load burden is shared among both HPS so voltage deviation on HPS_{1} and HPS_{2} are observed as 5.81V and 4.19V respectively. Figure 15 represents deviations on both HPS in stateII and stateIII. Total overloading of 50% in stateII and 11.11% in stateIII are shared with both HPS to get the deviations within the prescribed limit.
In stateII the voltage deviation observed as 45V which is beyond threshold (+40V) for conventional control while for multivoltage control the deviations observed in HPS_{1} and HPS_{2} are 18.87V and 26.13V which are under the threshold limit. As the voltage deviation in both the HPS with heavy overloading conditions are under the permissible limit with multivoltage controller so it results in good dynamic performance of the system. Table 3 shows the deviation of voltage for HPS_{1} and HPS_{2} with conventional control and multivoltage control under caseI and caseII.
Results of conventional control indicate that overloading on HPS_{2} is not shared by HPS_{1} in conventional control that’s why large voltage deviation is observed in HPS_{2} while there is no deviation in HPS_{1}. With the application of multivoltage control the overloading of HPS_{2} is shared by HPS_{1} causing a slight voltage deviation in HPS_{1} also the voltage deviation of HPS_{2} is reduced as compared to conventional control. Here overloading is shared by HPS_{1} and HPS_{2} in proportion to 42% and 58% respectively. This makes the system reliable for variation in loading conditions. Table 4 shows the %overloading shared by both HPS under conventional control and multivoltage control.
Table 3. Deviation of voltage in volts for individual and multivoltage control
Case 
Time (sec.) 
Conventional Control 
MultiVoltage Control 

HPS_{1} 
HPS_{2} 
HPS_{1} 
HPS_{2} 

CaseI 
t=0.5 
0 
30 
12.58 
8.39 
t =1 
0 
20 
17.42 
11.61 

CaseII 
t =0.5 
0 
45 
18.87 
4.19 
t =1 
0 
10 
26.13 
5.81 
Case 
Time (sec.) 
Overloading 
Single Frequency Control 
Multifrequency Control 

HPS_{1} 
HPS_{2} 
HPS_{1} 
HPS_{2} 
HPS_{1} 
HPS_{2} 

I 
t=0.5 
0KW 0% 
30KW (33.33%) 
0KW (0%) 
30KW (100%) 
12.58KW (42%) 
17.42KW (58%) 
t =1 
0KW 0% 
20KW (22.22%) 
0KW (0%) 
20KW (100%) 
8.39KW (42%) 
11.61KW (58%) 

II 
t =0.5 
0KW 0% 
45KW (25%) 
0KW (0%) 
45KW (100%) 
18.9KW (42%) 
26.1KW (58%) 
t =1 
0KW 0% 
10KW (16.7%) 
0KW (0%) 
10KW (100%) 
4.2KW (42%) 
5.8KW (58%) 
Intertied HPS control has a wide scope in real world due to its extensive applications. Various case studies have been performed to evaluate the efficacy of proposed method. Following conclusions have been drawn from the research.
(I) Till now the research has been focused on single frequency AC HPS and single voltage DC HPS. In this perspective a standalone multifrequency, multivoltage intertied HPS has been proposed in this study to assure uninterrupted power supply.
(II) It has been revealed from Table 1 that under heavy overloading the deviation in frequency is greater than prescribed limit and shows failure of single frequency control however for multifrequency control causes the deviation to distribute among HPS. This shows the applicability of the proposed method for heavy loading conditions.
(III) The proposed multivoltage control offers less deviation in voltage than conventional control with heavy loading condition as seen from Table 3 and achieves better performance in comparison to conventional control.
The proposed multifrequency, multivoltage droop control achieves better performance by sharing the overloading in respect to correction factor and assures frequency and voltage deviation under prescribed limit. The proposed method is coordinated, autonomous, simple, reliable and ease of implementation.
f 
frequency 
H_{p}^{total} 
Total load capacity 
H_{p}^{c} 
Critical load capacity 
i_{d1}^{ref} 
Direct axis reference current of HPS_{1} 
i_{q1}^{ref} 
Quadrature axis reference current of HPS_{1} 
i_{d1} 
Measured direct axis current of HPS_{1} 
i_{q1} 
Measured quadrature axis current of HPS_{1} 
k_{p} and k_{i} 
PI parameters 
P_{dc} 
Active power of DC HPS 
P_{ac} 
Active power of AC HPS 
Q^{ref}_{ac_1 } 
Reference reactive power of HPS_{1} 
Q_{1} 
Measured reactive power of HPS_{1} 
r 
Droop coefficient of DC HPS 
u_{d1and }u_{q1} 
Output signals of current control loop 
v_{cb} 
Common bus voltage 
v^{ref}_{dc} 
reference dcvoltage 
v_{dc} 
measured dcvoltages 
Greek symbols 

δv 
Correction factor for voltage 
δf 
Correction factor for frequency 
α_{p} 
Correction factor for p^{th} AC HPS 
α_{q} 
Correction factor for q^{th} DC HPS 
Subscripts 

p 
p^{th} AC HPS 
q 
q^{th} DC HPS 
* 
Rated values 
max 
Maximum value 
min 
Minimum value 
d 
Direct axis 
q 
Quadrature axis 
1 
HPS_{1} 
2 
HPS_{2} 
‘ 
Normalized value 
ac 
AC HPS 
dc 
DC HPS 
(1) System Parameters.
Controller 
HPS and IPC controller 

Controlling Parameter 
Value 

Voltage controller 
DC IPC K_{p} 
0.6 A/v^{2} 
DC IPC K_{i} 
50A/v^{2}s 

AC IPC K_{p} 
0.8 A/v 

AC IPC K_{i} 
100 A/vs 

Current Controller 
DC IPC K_{p} 
3 v/A 
Coordinated Power control 
Coefficient 
α_{1}=4, α_{2}=0.75 
K_{p} 
0.03 Hz 

Ki 
3Hz/s 
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