Three cases are investigated in this section. The results of these cases are presented and discussed here. The reactive power limits of conventional generators and the reactive power capability of large-scale solar photovoltaic (SPV) system have been put into consideration in this study. For the continuation power flow study, the load increase is uniformly distributed for all the load buses and the loads are modelled as constant PQ load. The values of the active and reactive power of the load utilized in this work are specified in Table 1.
Scenario 1: without shunt reactors
The voltage profile for each bus when no shunt reactor or any reactive power compensation device is utilised is presented in this section. The voltage profile for this base case scenario is shown in Fig. 5. The dashed, solid, and dotted red lines indicate the 0.95 pu, 1.05 p.u and 1.1 p.u voltage levels respectively. The figure reveals that overvoltage condition occurs in some buses, particularly in the Northern areas. This is due to the boost in the reactive power along the considerably long transmission lines connecting the central region to the Northern areas and the lightly loaded conditions of the Northern buses. This explains the reason for the use of shunt reactors in the Nigerian system. Shunt reactors absorb excess reactive power in order to keep the bus voltages at an acceptable level. With the highest voltage reaching as high as 1.86 p.u, the grid is forced to shut down. There are reported cases of deliberate grid collapse initiated by the National Control Centre, Oshogbo, because of sudden, dangerous overvoltage occurrence. Thus, the present Nigerian grid cannot safely operate without the application of any reactive power absorbing device, such as shunt reactors.
Bus voltage profile of the Nigerian 52-bus system without shunt reactors.
Scenario 2: shunt reactors applied in five locations
In this second scenario, we consider the effects of shunt reactors on the system’s voltage stability. This is the present case of the Nigerian grid. Shunt reactors are used to absorb the excessive reactive power, which produces overvoltage issues in the Northern buses. Figure 6 shows the bus voltage as determined from the load flow study of the system when shunt reactors are employed in five locations (Kaduna-75MVAR, Kano-75MVAR, Gombe-100MVAR, Yola-100MVAR and Maiduguri-75MVAR). It can be observed that the overvoltage issue in the base case scenario is significantly mitigated. However, the voltage levels at buses 19 (Gombe), 20 (Yola), 33 (Damaturu), 34 (Maiduguri) and 35 (Jalingo) still exceed 1.05 p.u, but not much beyond 1.10 p.u. This is still consistent with the overvoltage occurrence in Northern Nigeria. Thus, with the use of shunt reactors at Kano, Yola, Kaduna, Maiduguri, and Gombe, only one of the bus voltage levels slightly exceed 1.10 p.u as depicted in the figure. The voltage level at Jalingo, which is 1.1023 p.u is the highest. However, the performance of the shunt reactors is not fully satisfactory, coupled with the fact that the shunt reactors presently in use in Nigeria are aged and subject to frequent failures.
Bus voltage profile of the Nigerian 52-bus system with shunt reactors at five locations.
Furthermore, P–V and Q–V curves analyses are carried out to determine the critical loading limit and the reactive power margin of the system respectively. Figure 7 depicts the P–V curve for the most critical buses, which are in the Northern areas. The figure shows that with a base case total active load demand of 3658 MW, the total critical active power demand is 5028 MW and the tangent vector analysis of the P–V curves shows that Jalingo bus (bus 35) is the weakest bus in the system, followed by Yola, Maiduguri, Damaturu, Gombe, Jos, Makurdi, Aliade, Kano and Kaduna in that order.
P–V Curves for the critical northern buses.
The Q–V curve results also indicate that Jalingo has the smallest RPM (139.57MVAR) and the most negative CVQR of − 0.459. This shows that Jalingo bus is the weakest bus in the expanded 52-bus Nigerian 330 kV Power Grid. This result is similar to the weakest bus identification carried out in56 using eigenvalue method, where the Jalingo bus was also identified as the critical bus in the 330 kV, 52-bus Nigerian power grid. Table 2 shows the first ten weakest buses according to the tangent vector, reactive power margin and CVQR index rankings. This table gives a baseline comparison of the derived indices used in this work and the significant agreement in the bus rankings provides a basic validation for these methods. These results invariably show that buses in the northern parts are the weakest in the Nigerian power grid in terms of active and reactive power loadability margins. This is because these buses are largely distant from the southern buses where generating stations are concentrated.
Scenario 3: large-scale solar PV integration in the northern region
In this scenario, we investigate the possibility of utilising large-scale solar PV integration to enhance the voltage stability of the Nigerian grid while meeting the rising energy demand of the country. Two cases are considered here. In the first case, large-scale solar PV generation is located at Jalingo, since it has been determined as the weakest bus of the system, and the state where Jalingo is located has been reported to be suitable for solar power generation. In the second case, solar PV is distributed throughout selected buses in the Northern region, where there is abundant solar resource. The solar PV is modelled as a generator (PV) bus in this analysis. The reactive power limits of conventional generators and the reactive power capability of large-scale solar photovoltaic (SPV) system have been put into consideration in this study. Details of the reactive power control and capability characteristics of both the conventional synchronous generator and the SPV system have already been presented in17.
Solar PV located and centralized at Jalingo
The impact of increasing Solar PV penetration at the Jalingo bus on the voltage stability of the system has been carried out in this section. The Solar PV integration is examined for penetration levels ranging from 100 MW (2.65% PL) to 1000 MW (26.29% PL). The impact of increasing SPV penetration on the bus voltage profile is carried out with load flow studies. In addition, the effects of the increasing PL on the voltage stability margins of the SPV-connected grid are assessed with P–V and Q–V methods. The P–V analysis gives the total active power margin of the system and the Q–V study provide the reactive power margin and the CVQR index of the system for each investigated penetration level.
The impact of increasing SPV PL on the highest bus voltage within the system is illustrated in Fig. 8. The figure indicates that the highest bus voltage decreases as the SPV PL increases and falls within 1.0 ± 0.05 p.u at about 26.29% PL (1000 MW). This implies that the optimal SPV PL at Jalingo bus that will not lead to voltage limit violation at any bus is 1000 MW. Further increase in SPV PL at Jalingo bus results in low voltage condition (bus voltage less than 0.95 p.u) at Jos, Gombe, Yola, Damaturu and Makurdi. Since low bus voltage is undesirable, the SPV PL at Jalingo should not exceed 1000 MW.
Impact of increasing SPV penetration on highest bus voltage.
The reactive power absorbed/injected by the SPV at base case loading condition (λ = 0) and at maximum loading condition (λ = λmax) is depicted in Fig. 9. The figure shows that the SPV absorbs reactive power from the system at base case loading in order to regulate the bus voltages. The reactive power absorbed by the SPV is highest at 10.78% PL. After this point, the reactive power absorbed continues to decrease with increasing SPV PL in order to ensure that the system does not suffer voltage collapse due to declining reactive power in the system. At 26.29% PL, the SPV injects about 126.4MVAR into the system in order to sustain the voltage stability of the grid at this high penetration level. During maximum loading of the system as indicated by λ = λmax line in Fig. 9, the SPV injects reactive power into the system at each SPV penetration level so as to give voltage support to the system.
Reactive power injected by the SPV.
The megawatt margin and the lowest reactive power margin of the system with respect to increasing SPV PL are shown in Fig. 10a and b. As illustrated in Fig. 10a, the megawatt margin of the system continues to improve significantly as the SPV penetration level increases. Figure 10b indicates that the minimum reactive power margin of the system initially improves with increasing SPV PL and peaks at 10.78% SPV PL. This corresponds to the point at which the reactive power absorbed by the SPV is highest as depicted in Fig. 9. Thereafter, the RPM begins to decline and it returns to its original base case value at 18.72% (700 MW). The red dotted line in each figure indicates the original base case value. The RPM falls to a value of 176.3MVAR at the last investigated SPV PL of 26.29%.
Variation of megawatt margin and reactive power margin with SPV PL.
The corresponding CVQR of the system associated with the minimum RPM is shown in Fig. 11. The figure shows that the voltage stability of the system is initially improved as indicated by CVQR value becoming less negative. However, the CVQR begins to become more negative after 10.78% SPV PL, and returns to its original value at about 25.6% SPV PL. It can be observed from Figs. 10 and 11 that although the loadability of the system is increasingly enhanced with increasing SPV PL as indicated by the MWM of the system, the RPM and the CVQR of the system declines at higher SPV PL, thereby showing that the system tends toward voltage instability at higher SPV PL.
Variation of CVQR index with increasing SPV PL.
Solar PV located at weakest buses in the northern region
In this case, the SPV is dispersed across the weak Northern buses. SPVs are located in Jalingo, Maiduguri, Yola, Gombe, Damaturu, Kano, Jos, Kaduna and Birnin-Kebbi in an incremental manner. The Solar PV integration ranges from 100 MW (2.65% PL) to 1800 MW (46.81% PL) for this case.
Figure 12 shows the variation of the highest bus voltage with respect to the SPV PL. The figure depicts that the highest bus voltage decreases as the SPV PL increases. The bus voltage criterion of 1.0 ± 0.05 p.u is achieved at about 21.44% PL (about 800 MW). Thus, with 200 MW SPV integration at Jalingo, Maiduguri, Yola and Gombe each, a satisfactory voltage profile can be attained, with additional advantages as compared to the use of shunt reactors. As observed from Fig. 12, SPV PL of 13.49% (500 MW) at three locations will ensure that no bus voltage exceeds 1.102 p.u, which is the maximum performance obtained from the use of shunt reactors at five locations as discussed in “Scenario 2: shunt reactors applied in five locations” section.
Impact of increasing SPV penetration on highest bus voltage with SPV located at selected Northern buses.
Figure 13 shows the variation of reactive power injected/absorbed by the SPVs as the PL increases. The figure shows that the SPV absorbs reactive power at nominal base case loading (λ = 0) and injects reactive power at maximum loading point (λ = λmax) for all SPV PLs.
Reactive power absorbed/injected by the SPVs.
In Fig. 14a and b, the MWM and the minimum RPM of the system with respect to increasing SPV PL are illustrated. The figure shows that both the MWM and the RPM improves with increasing SPV PL. This is an additional benefit of employing large-scale SPV in various locations of the Northern region. Moreover, for this case, the corresponding CVQR of the system associated with the minimum RPM shown in Fig. 15 indicates that the voltage stability of the system is significantly improved as the SPV PL increases. Thus, this distributed SPV case offers a better voltage stability improvement than when SPV is located and lumped only at the Jalingo bus.
Variation of megawatt margin and reactive power margin with SPV PL.
Variation of CVQR index with increasing SPV PL.