Modeling and Analysis of the Dynamic Response of an Off-Grid Synchronous Generator Driven Micro Hydro Power System

This paper models and analyses the dynamic response of a synchronous generator driven off-grid micro hydro power system using Simulink tool of MATLAB software. The results are assessed from various perspectives including regulation through no load to full load and overload scenarios under normal and abnormal operating conditions. The investigation under the normal conditions of no load, linearly changing load and full load divulges that the system operates in a satisfactory manner as generator voltage and frequency remain approximately constant at 1 pu. However, at full load generator voltage and frequency drop 3% and 0.5% respectively from its nominal values but remain within prescribed standard IEC limits. The results also expose that the abnormal conditions produced by abrupt changes in load, system faults and severe overload, cause the unwonted variations in the magnitude of generator parameters. Moreover, the study reveals that the system stability significantly enhances when the system is run at full load because the regulation time to fix the variations in the generator parameters; except input mechanical power; decreases, e.g. from 4.1 sec to 0.8 sec for generator voltage, with the increase in the loading from quarter to full load respectively at unity power factor. Further, it is also observed that the regulation time rises, e.g. from 0.8 sec to 1.3 sec for generator voltage, with the reduction in load power factor from unity to 0.8, respectively. Thus, proper protection, to cater for increased fault current at full load and power factor correction must be provided to improve the system stability and protection. Furthermore, it is also concluded that the over loading in any case should be strongly avoided in this type of system and it should never be allowed to exceed 20% of the full load value to avoid system failure.


Introduction
Out of 7.795 billion people in the world (Sohani and Hoseinzadeh et al., 2021), still 840 million people have no access to electricity (World Bank, 2019) in which 87 percent currently are living in isolated and rural settlements. The electricity coverage gap among rural and urban areas in many parts of the world (United Nation, 2019) reveals that the pace of electrification to rural communities has remained painfully slow. This is because attention is usually paid to urban regions, rather than the rural communities. Consequently, most people residing in rural areas are backward in social and economic aspects (Akinyele et al., 2013;Akinyele et al., 2014). The foremost reason of this energy access gap between rural and urban regions, is that it is uneconomical to extend electricity grid infrastructure to remote communities owing to the low Amongst all sources of renewable energy, hydro power is the most beneficial source and has negligible social and environmental impact, compared to other renewable energy forms (Arabatzis and Kyriakopoulos et al., 2017). Micro hydro is a type of hydroelectric power that typically generates from 5 kW to 100 kW of electricity using the natural flow of water (Hoseinzadeh et al., 2020). It is the low cost, small size and can be installed to serve a small community making its implementation more appropriate in the socio-political and environmental context (Nasir, 2013). Micro hydro power (MHP) systems are usually runof-river systems which require very small flow of water with little or no requirement of water reservoir (Ali et al., 2017a;Ali et al., 2018a;Ali et al., 2018b;Ali et al., 2018c;Ali and Farooq, 2019). In addition, they have high efficiency range in between 70 to 90 percent (by far the best of all renewable energy technologies), high-capacity factor usually greater than 50 percent (in comparison to the 10% for solar and 30% for wind power plant) and less output power variations (Nasir, 2014).
For off-grid or stand-alone low power generation based upon MHP unit, the induction generator (IG) is considered more suitable than the synchronous one (Ion and Marinescu, 2013a;Ion and Marinescu, 2013b;Ion and Marinescu, 2012) because of its advantages like low price, robustness, reduced size, simple starting and synchronization, low maintenance, good response to faults and overloads and no need of external DC power supply when capacitors are used for excitation (Ion and Marinescu, 2011;Raza et al., 2013). However, for the low power range of few kW, induction machines are not manufactured specifically to operate as generators thus, series induction motors are employed as generators (Smith, 2008;Ion and Marinescu, 2013c). The drawback of the IG is the lagging power factor because the machine is magnetized from the stator (Ali and Farooq, 2019;Jussi, 2006) resulting in less power availability at a given current in comparison to synchronous machine (Ali and Farooq, 2019;Reljić, 2010). In addition, it shows poor voltage and/or frequency regulations when used for the development of micro hydro power systems specifically in self-exited mode (Saket and Varshney, 2012;Singh and Tiwari, 2013;Meshram et al., 2013;Scherer et al., 2013;Kathirvel et al., 2015). In contrast to IG, the use of synchronous generator (SG) at low power generation is very rare as it represents a high cost compared to the entire system cost; making its application, sometimes, economically unviable (Scherer et al., 2013). Despite this fact, the MHP systems using SG can be considered the most consolidated one, because of the features associated with the high performance of the technologies applied on its control (Scherer et al., 2013;Scherer and de Camargo, 2011;Ali et al., 2017b). Therefore, the proposed study considers SG for the development of an off-grid MHP system because of its several technical advantages over IG in terms of voltage control (Scherer et al., 2013;Scherer and de Camargo, 2011;Awad et al., 2005).
The focus of the presented work is to examine the dynamic response of synchronous generator driven micro hydro power system working in off-grid mode under normal and abnormal operating conditions. The normal conditions considered for the investigation are no load, linearly changing load and full load. Transient disturbances due to system faults and quick changes in load and severe overload are considered as abnormal conditions in the present analysis. This paper gives the full detailed modeling of proposed off-grid MHP system deploying SG. The investigation is carried out through digital simulations from various perspectives including regulation for no load to full load and no load to overload scenarios using Simulink tool. Simulink is a MATLAB based graphical block diagramming tool. It is commonly being used as experimenting tool for modeling, simulating and analysing energy systems (Nezhad and Hoseinzadeh, 2017). It has customizable built-in blockset libraries that makes it an attractive choice for hydroelectric systems' modeling and research (Simani et al., 2014;Simani et al., 2017). Alternatively, DIgSILENT PowerFactory tool can also be used for hydroelectric power systems' modeling and simulations (Olulope et al., 2013) but Simulink is widely used from last two decades for the non-linear dynamics research in hydro power plants (Mahmoud et al., 2004;Fang et al., 2008). As the alternate softwares also comply with the standards, the simulation results would be similar.

Micro Hydro System General Layout
The general layout of a typical micro hydro system is shown in Fig. 1. The basic components include the weir, desilting tank, penstock, turbine and generator (Michael and Jawahar, 2017). The water from the river or stream is diverted through an intake at the weir, which then enters to a desilting tank where impurities and debris are separated in it. Sometimes, a forebay tank is also located between the intake and penstock to store the water to maintain the constant head (Ali et al., 2018b). Then, water from the forebay tank is conveyed to a turbine through a pipe termed as penstock. The turbine converts the potential energy of the water into mechanical energy and the produced mechanical energy by the turbine is then converted into electrical energy with the help of a generator.
Theoretically, the hydraulic power ( "#$ ) available from a micro hydro source is determined using the following mathematical relation (Ali et al., 2018a;Ali and Farooq, 2019).
Where , , and represent water density, gravitational constant, effective flow rate and head, respectively. This hydraulic power is normally reduced by the efficiencies of the system's components including the turbine and generator. When the hydraulic power in (1) is multiplied by overall efficiency ( ) of an MHP unit, gives the final output electrical power (Ali and Farooq, 2019):

System Formation and Specifications
Fig. 2 depicts the formation of proposed off-grid MHP system, taken into consideration for dynamic analysis. A variable speed micro hydro turbine drives the DC excitation based synchronous generator of 400 V, 85 kVA capacity. The electrical power generated by the SG is then distributed to sparsely scattered load through a short power line network.

System Modeling with its Components
The comprehensive model considered in this paper for the modeling and analysis of proposed MHP system, is illustrated in Fig. 3. The SG is driven by variable speed MHP turbine and is connected to off-grid load through a power line. A speed governor is used to control the speed of the micro hydro turbine. The field voltage of the DC exciter is controlled by a regulator so as to supply the balanced power to varying load. The detailed mathematical representation of all the components used in this model is discussed in the subsequent sections.

Modeling of Hydraulic Turbine with a Penstock
Mathematically, a penstock pipe of length and crosssectional area is expressed in equation as (IEEE Working Group, 1992): Where 1 and 3 are static head and head loss in penstock, respectively. For rated power output, the per unit representation of (3) is given using base flow ( 6789 ) and base head (ℎ 6789 ): Where , ℎ and ℎ 3 represent per unit value of , and 3 , respectively. The (4) can also be represented with water time constant. While the water time constant ( = ) is mathematically expressed as (IEEE Working Group, 1992): Therefore, the (4) becomes as: The hydraulic turbine is basically represented by its hydraulic characteristics and output mechanical power. The per unit flow rate through the turbine is given by (IEEE Working Group, 1992): = √ℎ (7) Where in (7) represents the gate position or opening. From a micro hydro source, the produced mechanical power by a turbine is the product of water effective flow rate and rated head, but this power is decreased by a factor, to account for the turbine losses. Another important factor i.e., speed deviation damping effect , must also be included. Therefore, the turbine mechanical power ( C ) in per unit form is represented mathematically as (Ali and Farooq, 2019): Where D , E3 , and represent turbine gain, per unit no load flow, damping coefficient and speed deviation, respectively.
The turbine gain is calculated mathematically using full load ( F3 ) and no load ( E3 ) gate positions as (Kundur, 1994): The model of a hydraulic system with a turbine and a penstock having unrestricted head and tail race is shown in Fig. 4, which is obtained by combining the (6) for the penstock, and (7) and (8) for the turbine.

Modeling of Synchronous Generator
The modeling of synchronous generator is represented mathematically by expressing its electrical and mechanical characteristics. Using dq-axis transformation in the rotor reference frame, the machine's electrical part is represented. The equations of flux and voltage in this frame of reference are given as (Ahsan, 2013). The flux equations: The equations of voltage: Where quantities , , , , and from (10) to (21) represent the flux linkage, inductance, current, voltage, resistance and speed, respectively. In these quantities daxis, q-axis, d-axis field, d-axis magnetizing, q-axis magnetizing, stator and rotor components are represented by the subscripts , , , , , and , respectively. Whereas , 1 and 2 subscripts represent the dq-axis components of damper winding. While dq-axis damper winding and d-axis field winding leakage components are specified by the subscripts , 1, 2 and , respectively.  The mechanical part of the synchronous machine is mathematically represented by using equation of motion of the rotor as (Ahsan, 2013): Where C and 9 are the mechanical and electromagnetic torques respectively, S is the speed of rotor, is the coefficient of inertia, and represents the friction coefficient.

Modeling of Speed Governor
The electro-hydraulic type PID speed governor is used for the proposed system as it is flexible and offers better performance (Ali and Farooq, 2019).
While the values of governor time constants Ta, Tc and Td are set by the pressure/flow properties of the gate and its servos (Choo, 2007). The ] and c in (23) and (24) represent the transient droop and reset time, respectively.

Modeling of Excitation System
DC based excitation system is used for synchronous generator in the proposed off-grid micro hydro power system. Fig. 6 demonstrates the mathematical model of such excitation system whose basic components are a voltage stabilizer, a voltage regulator and a DC exciter (Ali and Farooq, 2019). Amongst voltage regulator time constants TA, TB, TC; TA is the key constant while others are normally small enough to be ignored (Ali and Farooq, 2019;IEEE Std 421.5-2005, 2006. The field voltage ( F ) at the output of exciter is mathematically related to regulator output voltage ( c ) as (IEEE Std 421.5-2005, 2006: Where, h is the exciter time constant and h represents the constant related to exciter self-excitation. Fig. 7 gives the mathematical model of terminal voltage transducer and load compensator model, adopted from (IEEE Std 421.5-2005, 2006. The prime input to the regulator of DC excitation system is the output voltage VC from this model.

Modeling of Remaining Components
The remaining components of the proposed system such as power line and load are modeled using built in block-sets of SimPowerSystems library of Simulink tool of MATLAB software.

Results
The proposed system model is simulated to test and to analyse the dynamic response of the SG driven off-grid MHP system from various perspectives including regulation under steady and transient states at various load changing scenarios from no load to full load and from no load to overload during normal and abnormal operating conditions. The normal conditions taken for the investigation are no load, linearly changing load and full load, while the abnormal conditions include the transient disturbances due to quick changes in load and the faults on the system, and severe overload. The response of the system is depicted in waveforms for the magnitude of generator current (Ig), magnitude of generator voltage (Vg), magnitude of generator frequency (fg) and magnitude of input mechanical power (Pm) against the magnitude of different load changing scenarios of active power (PL) and reactive power (QL), in per unit (pu) form.

Results During No Load to Full Load Scenario
System is tested through no load to full load under normal operating conditions, by varying the PL (active load power) at unity power factor by keeping the QL (reactive load power) equal to zero. The simulation is carried out for 60 seconds as depicted in Fig. 8. In the start, the generator is brought into motion without connecting the load i.e., machine is running at no load. The governor maintains the nominal speed, while excitation system adjusts the field voltage so that the generator produces nominal voltage at the nominal frequency. Thus, after attaining the nominal voltage and frequency, the load can be connected to SG. During no load to full load test, the QL is maintained to 0 pu, whereas only PL is varied from 0 pu (no load) to its maximum value of 1 pu (full load).

Results During No load to Overload Scenario
System simulation is carried out for 90 sec through no load to overload to test its performance from regulation viewpoint because of the transient disturbances due to rapid load changes and system faults. The results of this testing are shown in Fig. 9. Load changes are introduced at 10 sec, 30 sec and 50 sec through the combination of PL and QL as these are the inputs to generator. The generator is started with no load i.e., both PL and QL are zero, during this period, the SG produces nominal voltage (1 pu) at nominal frequency (1 pu). However, in the beginning when the machine starts, these parameters vary around the respective nominal values and then stabilize rapidly because of the control action of excitation and governor in MHP system. After achieving the nominal voltage and frequency, the load can be applied to SG. Therefore, at 10 sec PL increases to the half of its full load (1 pu), correspondingly QL increases to one-fourth (0.25 pu) of its full load (1 pu) at 30 sec such that the load power factor (PF) becomes 0.9. Congruently, at 50 sec PL raises to full load while QL increases to three-fourth (0.75 pu) of its nominal full load value, which reduces the PF of load to 0.8 from unity. While the transient instabilities due to faults are created at 20 sec, 40 sec and 65 sec on a 400 V line for 0.1 sec by a three-phase to ground fault. However, to examine the behaviour of the system during overload, from 80 sec onward the load on the system is successively raised from its full load value (1 pu).

Response Under Normal Operating Conditions
Under normal operating conditions, the simulation results of Fig. 8 indicate that the system remains stable and operates satisfactorily as Vg and fg maintain 1 pu value as the load increased linearly from no load to full load. However; at full load there is a slight decline of 3% and 0.5% in Vg and fg respectively which should not be a major issue considering the operation of system in isolated mode where synchronization with the grid is not reqired. In addition, these deviations in voltage and frequency are within the allowable limits of IEC standards (Nömm et al., 2018).

System's Response During Quick Changes in Load
The results of Fig. 9 reveal that the rapid changes in load (PL or/and QL) at 10 sec, 30 sec and 50 sec produce transients in the generator voltage, frequency and current which are regulated by the control actions of the MHP system. Further, it can also be seen in the waveforms that the generator voltage and frequency slightly fall from the respective nominal value during the steady state period at full load with 0.8 PF. Whereas, the input mechanical power also drops at the occurrence of these transients caused by rapid changes in load and then varies close to its nominal value in order to adjust the output electrical power to meet the load changes or demand.

System's Response During Faults
The simulation results of Fig. 9 also describe the dynamic response of the system under the abnormal condition of transient disturbances caused by a three-phase to ground fault at 20 sec, 40 sec and 65 sec when the system is running in steady state. The occurrence of faults on power line causes the generator current to rise very high as depicted in the third graph of Ig and the magnitude of this fault current becomes very high for the transient that occurs when the MHP system is feeding the large load.  Fig. 9 illustrates that on the fault occurrence, the generator voltage drops to 0 pu and quickly restores to its steady state value as the fault is cleared and this situation is also shown in Fig. 10 at the incidence of transient at 65 sec. The rapid restoration of the generator voltage is because of the field voltage of excitation system that is controlled by a regulator to maintain the nominal voltage of generator. Besides, the frequency of the generator also falls on the occurrence of fault as shown in the graph of fg and then it oscillates around its nominal value of 1.0 pu as the speed governing system of MHP system normalizes it after the fault clearance. Whereas the graph of Pm in Fig.  9 indicates that the input mechanical power shows a decline before the clearing of fault and then varies increasingly to reach toward its steady state value.

System's Response During Overload
The waveforms of Fig. 9 also depict the results of simulation under abnormal condition of overload at 80 sec which expose that the MHP system cannot maintain the voltage and frequency, if the load is increased above its nominal full load value i.e., 1 pu. The first graph of PL shows the load increment in ramp fashion from 80 sec ahead. When the load active power crosses 1.2 pu, the generator current increases abruptly, and the voltage and frequency go down speedily, and at this time the input mechanical power takes a dip and then rises to balance the increasing load but again immediately drops to 0 pu and the system finally collapses.

System's Regulation Response During Transients
The graphs of Fig. 9 also show that the respective regulation time to stabilize the generator current, generator voltage and generator frequency and input mechanical power is relatively much high for fault transients as compared to transients caused by load changes, as recorded in Table 1. Moreover, the regulation time for these parameters decreases with the increase in loading on the MHP system, while the input mechanical power shows the contrary behaviour to this. However, the regulation time for these parameters increases at load with lower PF as compared to the same load with unity PF. Furthermore, the Ig, Vg and fg graphs in Fig. 9 also divulge that upon transient the generator current takes much longer time to become steady as compared to generator voltage and frequency. The time of regulation for transient disturbances caused by system faults under various simulation scenarios at different loading conditions are summarized in the Table 2 which shows that the recovery time for Ig, Vg and fg decrease with the increase in the loading except Pm. However, the magnitude of the fault current increases with the rise in loading on the MHP system as discussed already.

Technical Findings and Suggestions
This investigation finds that the MHP system works satisfactorily and in a stable fashion under the normal operating conditions. However, under abnormal operating conditions, the results depict the unwonted variations in system parameters include generator current, voltage, frequency and input mechanical power. Moreover, the respective regulation time to stabilize the generation parameteres is relatively higher for fault transients as compared to transients caused by load changes. Further, the regulation time to fix the variations in these parameters decreases with the increase in loading on the MHP system except input mechanical power that shows the contrary behaviour. Therefore, it is suggested to operate the SG driven off-grid MHP system preferably at full load. However, the appropriate protection scheme against the increased fault current must be provided to protect the system as the fault current increases in this type of system with the increase in loading. In addition, the time of regulation is increased when the power factor of the connected load on the proposed MHP system decreases from unity. Hence, it is recommended to provide appropriate PF correction to confirm the lower regulation times as well as fault current. This will also ensure the decrease in the time for which fault current flows in the network enhancing system stability and protection. Furthermore, it is also concluded that the system over loading equal or above the 1.2 times of the full load can collapse the system. Therefore, it is highly advised that the over loading of the system should be avoided in any case.

Future Research and Scope
The electrical energy storage (ESS) systems are the backbone of a stand-alone renewable power generation systems, which helps to provide a secure and reliable power supply. The operation of stand-alone or off-grid renewable power generation systems without energy storage is affected highly due to intermittent nature of generation and sudden load demand fluctuations. Of all small scale ESS options, battery based storage systems are considered more efficient in terms of scalability, efficiency, lifetime, discharge time, weight and mobility of the system (Kyriakopoulos et al., 2016). Thus, combining proposed MHP system with batteries or other possible ESS options suggests area for future research whose viability need to be explore under similar or different circumstances.