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ESS can absorb excess energy during off-peak times and inject the stored energy when needed during the system peak. The storage devices can also support the grid in case of power system contingencies.

In some networks, the peak demand occurs only for a short period of time

Using energy storage to defer infrastructure investment

by TM Bengani and JA Kombe, Eskom

Electricity utilities are faced with a number of challenges relating to network infrastructure expansion. The common challenges are funding constraints, inability to obtain servitudes/right of way (ROW) in time, demand growth uncertainty and life extension of existing infrastructure. Energy storage systems (ESS) represent opportunities to reschedule large investment in the network infrastructure.

during the day (low load factor supplies), but the grid is planned and designed to accommodate the peak demand. In such instances, ESS is a feasible alternative to the traditional approach of increasing capacity to meet the peak demand. The ESS units are modular and can be deployed with little effort in the network.

Hence, they can be used to alleviate grid congestions until a network strengthening plan can be implemented.

Optimal sizing and placement of the ESS in the power system is an important aspect to maximise the benefits of the ESS in the system. Sub-optimal placing and sizing of ESS can cause thermal and voltage problems in the network [1]. According to literature, the widely used methods to optimise the size and location of the ESS in the network are based on optimisation techniques. Optimisation techniques are well-suited for optimising the size of the ESS, but their capability regarding choosing the optimal placement of the ESS in the network is not very clear.

We propose using power-voltage (P-V) curves and modal analysis to optimise the location of the ESS on the network, especially in interconnected systems. The proposed method is based on knowledge from the location optimisation of react ive power compensat ion devices and distributed generators in a constrained network. This method is most relevant to networks experiencing thermal overloading and/or low voltage conditions. The study focuses on using ESS as an intermediate solution to address network constraints until capital and/or servitude challenges are resolved.

Energy storage systems

Energy storage systems can perform many different functions on the electrical network. These include peak shaving, voltage regulation, frequency regulation, spinning reserve, and aiding the integration of renewable generation by mitigating their intermittency effects. These applications serve to increase the reliability and stability of the grid.

To maximise the benefit of the ESS in the network, it is important to optimise its size and location. Modal analysis (Eigen values and participation factors) was used to determine the optimal location Fig. 1: Flow chart describing the process followed in the case study.

GENERATION

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Fig. 2: Daily load profile.

for the ESS. This method is widely used in optimising the location of reactive power compensation and distributed generators in the network.

Placement of the energy storage systems

The optimal placement of the ESS in the network is an important aspect to maximise the benefits of the ESS in the system. The main steps are detailed in the subsequent subsection.

Modal analysis

The modal analysis technique is one of

the voltage stability margin evaluation methods. It uses the reduced Jacobian matrix to analyse the system and provides both relative proximity of the system to voltage insecurity, as well as the mechanism or key contributing factors to insecurity. The linearised steady state system power voltage equations are given by [2, 3, 4, 5, 6].

where:

∆P = incremental change in bus real power.

∆Q= incremental change in bus reactive power injection.

∆θ= incremental change in bus voltage angle.

∆V= incremental change in bus voltage magnitude.

JPθ, JPV, JQθ and JQV are Jacobian sub-matrices representing the sensitivities of active and reactive power with respect to voltage angles and magnitudes. J is Jacobian matrix of the power system. The reduced voltage angle and magnitude Jacobian matrices can be defined as:

where:

JRQV is the reduced Jacobian matrix containing the Q and V. On the other hand, JRPθ is the reduced Jacobian matrix containing the P and θ. Information about system voltage stability can be obtained from these matrices in both perspectives: reactive and active power conditions.

However, matrices J, JRQV and JRPθ are singular at the same point, the same modal information obtained from J, at its singularity point can also be obtained from JRQV and JRPθ. Modal analysis applied to reduced or unreduced Jacobian matrices results:

(6)

where:

θ – Contains the right eigen vectors of matrix J;

Fig. 3: Study area network diagram.

Table 1: Limiting contingencies to the base case.

Table 3: Bus participation factors to contingency D3-D4.

Contingency Load (MW) Violation

T1–D3 189 Voltage

D4-D3 189 Voltage

Contingency: T1-D3

Eigen value = 0,073469

Bus participations

Bus Participation factor

D8 1,00000

D7 0,99354

D9 0,86911

D6 0,82890

D5 0,76030

Contingency: D4-D3

Eigen value = 0,057964

Bus participations

Bus Participation factor

D8 1,00000

D7 0,99609

D9 0,90619

D6 0,87947

D5 0,82865

Table 4: Bus participation factors to contingency D4-D5.

Table 2: Bus participation factors to contingency T1-D3.

Contingency: D4-D5

Eigen value = 0,038552

Bus Participations

Bus Participation factor

D5 1,00000

D6 0,95347

D7 0,63421

D8 0,39161

D9 0,17738 (1)

(2)

(3)

(4)

(5)

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Γ – Contains the left eigen vectors of matrix J;

Λ – Contains the eigen values of matrix J.

The bus participation factors are used to identify buses vulnerable to voltage collapse and locations where injections of power benefit the system most. They provide ranked list of bus participations for each computed mode. The locations with high participation factors are the most suitable candidates for ESS installation. These are generally the buses prone to voltage instability due to the lack of reactive power support (weak buses). It is important to note that weak buses are not necessarily the ones with the lowest voltages.

Process

The process in Fig. 1 was followed to compute the load flows, P-V analysis and modal analysis.

Sizing energy storage systems

The sizing of the ESS depends on a number of factors, including but not limited to the years intended for the capacity upgrade deferral, expected load growth, equipment rating, existing loading conditions, and the shape of the load profile. Its capacity is measured in two dimensions, i.e., power capacity and energy capacity, respectively. The power capacity is represented by the maximum discharging power and the maximum charging power. On the network, the power capacity is relevant to the possible maximum load and the transmission capability. The power output of ESS is positive when discharging, while negative when charging [7]. The active power size of the energy storage is given by [8].

(7)

where PBES(t) is the power size of the energy

storage in year t, Pload(t) is the expected

load at year t and Plimit is the rating of the ESS as shown in Fig. 2. The energy sizing of the ESS should be equivalent to the area under the dispatch curve during the peak day:

where EESS(t) is the energy rating of the

ESS to meet the load, and t represents the number of hours the ESS dispatches the energy.

Case study

The proposed methodology was applied in a 132 KV sub-transmission network

Fig.4:P-Vcurves.

Fig.5:ESSinstallationvsnetworkcapacity.

with long lines. The network and results are described in this section.

Network description

The area under study is supplied at 132 kV by two main transmission infeeds (T1 and T2) as shown in Fig. 3. T1 and T2 are situated approximately 160 and 180 km away from the load centre, respectively. The 132 kV network is run normally closed.

The sub-transmission network has over time become increasingly congested due to demand growth. It is constrained, particularly during peak hours when system voltages in some parts drop below acceptable levels, despite the availability of transmission and generation capacity at T1 and T2. The constraint is due to

inadequate reactive power supply in the load centre. To address the above, it was proposed that a transmission injection be introduced and integrated into the 132 kV network. These types of projects are prone to lengthy environmental processes and budgetary constraints. This creates challenges in executing projects and commissioning within the required time. The 132 kV network transfer capacity is 185 MW against a peak demand of 189 MW. The average projected regional demand forecast growth over the ten year planning period is 2,5%. This equates to the power demand of 214 MW in the fifth year and 236 MW in the nineth year.

ModalanalysisandP-Vcurvesresults

Power System Simulation for Engineering (PSSE) software was used for power flow

(8)

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analysis and Voltage Stability Assessment Tool (VSAT) was used for P-V curves and modal analysis. The simulations were carried out for pre- and post-fault conditions to assess the power transfer limit and voltage security of the system. Pre- and post-fault conditions were analysed and the power transfer limit and voltage level of the critical buses are evaluated. Modal analysis was also performed at the point of instability, one eigenvalue (mode) was analysed with its respective bus participation. The weakest buses are indicated by the highest bus participation factor.

First ESS placement

The first simulation is performed on the existing network to determine the power transfer limit of the network and to identify the location for the first ESS based on the N-1 contingencies. The worst contingencies and the corresponding modal analysis results are shown in Tables 1 to 3.

D7 and D8 have the highest participation factors, hence they are the weakest buses in the system; 10 MW storage units were installed at the two locations. This increases the power transfer limit from 189 to 221 MW, net increase of 32 MW. The next limiting contingency is now D4-D5. Since the transfer capacity has not been met over the study period, another ESS is, therefore, required.

Second ESS placement

Modal analysis is conducted after installing the two 10 MW ESS at D7 and D8 to determine the new eigenvalues and participation factors. The limiting contingency is D4-D5 as determined in the above step. The corresponding eigen

Fig.6:Netpresentvaluecomparison.

value and participation factors are shown in Table 4.

The participation factors for D7 and D8 improved after installing ESS at both locations. The next identified location is D5. Similarly, a 10 MW ESS is installed at D5 and the transfer limits are calculated. The additional ESS at D5 results in a net increase of 24 MW in power transfers. The new power transfer limit is 245 MW and the limiting contingency is T1-D3. The new limit can support the forecasted network demand up to the tenth year. In this instance, it means that the network infrastructure investment can be deferred by ten years by installing ESS at identified optimal locations in the network. Fig. 5 shows the improvements in power transfers as ESS are introduced into the network.

Fig. 6 depicts the forecasted demand against the network transfer limit. Furthermore, the installation of the ESS can be aligned with the network capacity requirements. This is particularly important in networks with uncertain demand growth.

Financial implications

The following financial parameters were assumed: 10,6% discount rate and an exchange rate of R12,56 per US$ in calculating the Net Present Value (NPV) of the project cost. The NPV of the three ESS installed are compared to the NPV of the original and the deferred transmission injection project as shown in Fig. 7.

The opportunity in costs between executing the project now and ten years later is the NPV difference between

“deferred” and “original” values, in this case, approx. US$51,8-million. This is the justifiable amount to allocate to an intermediate solution for this network. The NPV cost of the ESS is US$58,1-million, which is comparable to the justifiable amount.

Conclusion

A strong business case can be put forward to motivate the installation of ESS, as an intermediate solution, for a network based on a justifiable amount due to project deferral. The analysis revealed that modal analysis can assist network planners in identifying optimal locations to install ESS.

Acknowledgement

This article was presented as a paper at the PowerGen Africa and Distributech Africa 2018 Conference.

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Contact Jamila Kombe, Eskom, Tel 011 800-3300, kombej@eskom.co.za v