Reactive power deployment and cost benefit analysis in DNO operated distribution electricity markets with D-STATCOM

Abstract

The aim of this paper is to analyze unbalanced radial distribution systems (UBRDS) with the distribution static compensator (D-STATCOM). The main objectives of this paper are D-STATCOM allocation in UBRDS with an objective of providing reactive power support to enhance voltage profile and reduce line losses of the distribution network, determination of optimal D-STATCOM rating subjected to minimization of total cost, and impact of D-STATCOM placement on improving power factor and savings in cost of energy loss. The analysis is conducted on a large industrial load model with light, medium and high loading scenarios. Further, the impact of load growth is also considered for better planning of the power distribution system. The results are obtained on standard 25-bus UBRDS to check the feasibility of the proposed methodology.

Keywords

unbalanced distribution system / D-STATCOM / voltage sensitivity index / load models / load growth / distribution network operator (DNO)

Introduction

The loads of power systems such as motors, pumps, fans etc., are reactive in nature and demand reactive power. If the reactive power demand is not met due to varying operating conditions in the system, the voltage profile of the network may become poor. Studies show that 13% of the total power generated is wasted in distribution side as line losses [¹]. This loss may increase in the case of unbalance load due to extra circulating current. With the competitive structure of the power system adopted world-wide, the utilities are required to utilize the existing network optimally with the growing need of demand. The reactive power requirement with higher load demand may cause poor voltage profile if the reactive power deployment is not adequate.

The reactive support is thus identified as one of the important ancillary services that are to be supplied, operated and maintained by distribution network operators (DNOs) [²]. Thus, active participation of DNOs is necessary for effective governance of deregulated electricity market (DEM) with optimal recourse utilization. The main functions of DNO operated competitive reactive power market are reactive power procurement, monitoring and control, with efficient electricity market management [³]. Optimal load flow analysis (OLFA) is used to examine the voltage profile, and active and reactive power losses. Besides, it is essential to find the optimal location, the size, as well as the cost of reactive power sources [⁴]. In the deregulated environment, DNO ensures the actual reactive power output considering voltage security as well as line losses. DNO is responsible for providing MVAR support and its remuneration for capital and operational cost recovery of reactive support devices.

Various authors have worked for improving the voltage profile of the network by installing voltage regulator as well as capacitor bank to reduce the losses of the distribution system. But, the problems with voltage regulators are that it cannot generate reactive power and it is quite slow in response. Capacitors cannot generate variable reactive power. So, there is a need to look for an alternate option which can solve the problems and the solution is the custom power devices (D-STATCOM, DVR and UPQC) [⁵]. Researchers have worked with these devices and show that D-STATCOM is more appropriate since it provides low power loss, less harmonic production, high regulatory capability with low cost [⁶,⁷]. The D-STATCOM, a shunt connected voltage source converter has been utilized to increase the reliability and efficiency of distribution systems by providing reactive power to improve the voltage profile and to reduce the line losses under varying load conditions [⁸]. The modeling of shunt connected D-STATCOM and the series connected SSVR for distribution system load flow analysis is presented [⁹]. Two different conditions can be taken into account by DNOs with the aim of maximizing their benefits. The first one is that D-STATCOM is owned and DNO is allowed to acquire D-STATCOM and can make the most of the economic remuneration for distribution system investments. The second one is that unbundled DNO is prohibited to be the owner of D-STATCOM but it can take full advantage of the economic earnings, making an allowance for a number of incentives. The placement of D-STATCOM poses some challenges to DNOs such as power losses, voltage stability and its cost analysis. Three methods are used for optimal placement of reactive power sources to maximize its benefit which are sensitivity based analysis, cost benefit analysis and the voltage stability margin method [¹⁰]. The voltage stability indicator used for finding the weak bus of the radial distribution system (RDS) for the purpose of D-STATCOM placement is demonstrated in Ref. [¹¹]. An analytical approach is used for placement of D-STATCOM in RDS [¹²]. Recently, many algorithms like firefly algorithm [¹³], immune algorithm [¹⁴], particle swarm optimization algorithm [¹⁵], bat algorithm [¹⁶], bacterial foraging optimization algorithm [¹⁷], harmony search algorithm [¹⁸], improved cat swarm optimization [¹⁹], and variational algorithm [²⁰] have been used for D-STATCOM placement in balanced RDS with an objective of improving voltage profile and reducing losses. The exhaustive search method is used to find the optimal size of D-STATCOM in RDS [²¹]. Simultaneous placement of D-STATCOM and photovoltaic array in a reconfigured network using the fuzzy-ACO method is explained [²²]. The social spider optimization is used for finding the optimal location and best size of D-STATCOM considering the uncertainties of loads [²³]. The placement of D-STATCOM for reducing the losses of RDS is explained [²⁴].

Since the D-FACTS devices are costly and as an ancillary services support, these devices need to be remunerated. So, there is a need to perform the cost benefit analysis. Research has been conducted by many researchers for finding the optimal location and size of D-FACTS devices in balanced RDS with an objective of reducing the losses with improved voltage profile. But the study for placement of D-STATCOM is also needed in the three phase unbalanced distribution system. This paper presents an optimal placement of D-STATCOM in UBRDS with an objective of providing reactive power support to improve voltage profile and reduce line losses. The optimal location of D-STATCOM is selected based on VSI while the optimal rating of D-STATCOM is selected based on the variational technique subjected to minimization of total cost. The analysis has been performed on a large industrial load model with light, medium and high loading scenarios. Further, the impact of load growth is also considered for better planning of the power distribution system by DNOs.

Roles and responsibilities of DNO operated distribution system

The main responsibilities of DNOs are to manage the system to meet the power demand, dynamic scheduling, keep spinning reserve for backup supply, provide reactive power for better voltage management, provide facility for system black start, and to ensure network stability. The fundamental propose of DNO operated competitive reactive power market is to provide fair pricing mechanism to remunerate all reactive power sources [²⁵,²⁶].

For efficient, secure, and reliable distribution system operation, DNO has the major responsibilities as categorized in the four blocks in Fig. 1. DNO coordinates for the retail sale of the energy in real time energy market. It is responsible for maintaining the security and stability of distribution systems with proper voltage profile while meeting all power transfer obligations to different transactions. It has the responsibility to procure reactive power support for optimally deploying it in the system for maintaining the voltage profile and reduce losses in the system. For sustainability of the reactive power sources as ancillary service providers in the ancillary service market, DNO decides remuneration for their reactive power support [²⁷,²⁸]. This requires DNO to carry out analysis of the optimal reactive power dispatch with cost benefit analysis. In this paper, sensitivity analysis is conducted for optimal placement of D-STATCOM that can help DNO for better planning of reactive sources. The optimal reactive support is obtained for minimum losses in the system with voltage stability margin enhancement. Then, the cost benefit analysis is performed for remuneration of D-STATCOM.

Load flow analysis for unbalanced radial distribution system

A simple UBRDS is shown in Fig. 2. The load flow algorithm used in this paper consists of the forward and the backward sweep methods. The forward sweep is mainly a voltage drop calculation from the sending end to the receiving end of a feeder or a lateral while the backward sweep is primarily a current summation based on voltage updates from the far end of the feeder to the sending end. The steps involved in the load flow solution [²⁹] are explained below.

Load currents calculation

(1)I{L}_a[i]={\left[{\displaystyle \frac{P{L}_a(i)+jQ{L}_a(i)}{v_a(i)}}\right]}^{*},

(2)I{L}_b[i]={\left[{\displaystyle \frac{P{L}_b(i)+jQ{L}_b(i)}{v_b(i)}}\right]}^{*}

(3)I{L}_c[i]={\left[{\displaystyle \frac{P{L}_c(i)+jQL(i)}{v_c(i)}}\right]}^{*},\hspace{0.17em}\mathrm{for}\hspace{0.17em}i=\mathrm{1},\mathrm{2},\mathrm{3},\dots ,n,

where IL_a, IL_b and IL_c are the load currents; v_a, v_b and v_c are the bus voltages; PL_a+jQL_a, PL_b+jQL_b and PL_c+jQL_c are the load demands in phases a, b and c respectively; and n is the total number of buses.

Backward sweep to sum up line section current: starting from the last branch and moving towards the root node, the current in branch I_br is

(4)I{L}_a(\mathrm{se}(k))=I{L}_a(\mathrm{se}(k))+I{L}_a(\mathrm{re}(k)),

(5)I{L}_b(\mathrm{se}(k))=I{L}_b(\mathrm{se}(k))+I{L}_b(\mathrm{re}(k)),

(6)I{L}_c(\mathrm{se}(k))=I{L}_c(\mathrm{se}(k))+I{L}_c(\mathrm{re}(k)),\mathrm{for}k=1,2,3\dots nb.

(7)I_{{\mathrm{br}}_a}=I{L}_a(\mathrm{re}),

(8)I_{{\mathrm{br}}_b}=I{L}_b(\mathrm{re}),

(9)I_{{\mathrm{br}}_c}=I{L}_c(\mathrm{re}),

where I_{{\mathrm{br}}_a},\hspace{0.17em}{I}_{{\mathrm{br}}_b},I_{{\mathrm{br}}_c}are the branch currents in each phase; nb is the total number of branches; and se and re are the sending and receiving end nodes, respectively.

Forward sweep to update nodal voltages: starting from the first node and moving towards the last node.

Voltage drops in each branch are

(10)\Delta V_a(i)=Z_{aa}(i)*I_{{\mathrm{br}}_a}(i)+Z_{ab}(i)*I_{{\mathrm{br}}_b}(i)+Z_{ac}(i)*I_{{\mathrm{br}}_c}(i),

(11)\Delta V_b(i)=Z_{ba}(i)*I_{{\mathrm{br}}_a}(i)+Z_{bb}(i)*I_{{\mathrm{br}}_b}(i)+Z_{bc}(i)*I_{{\mathrm{br}}_c}(i),

(12)\Delta V_c(i)=Z_{ca}(i)*I_{{\mathrm{br}}_a}(i)+Z_{cb}(i)*I_{{\mathrm{br}}_b}(i)+Z_{cc}(i)*I_{{\mathrm{br}}_c}(i).

The voltages at the receiving end node i is

(13)V_a(\mathrm{re}(i))=V_a(\mathrm{se}(i))-\Delta V_a(i),

(14)V_b(\mathrm{re}(i))=V_b(\mathrm{se}(i))-\Delta V_b(i),

V_c(re(i))=V_c(se(i))–V_c(i), for i=1,2,3,...,n.

(15)V_c(\mathrm{re}(i))=V_c(\mathrm{se}(i))-\Delta V_c(i),\mathrm{for}i=1,2,3,\mathrm{...},n.

Voltage deviations in the present and previous iterations are

(16)\mathrm{del}{V}_a=V_a-v_a,

(17)\mathrm{del}{V}_b=V_b-v_b,

(18)\mathrm{del}{V}_c=V_c-v_c,

(19)\mathrm{del}V=[\mathrm{del}{V}_a;\mathrm{del}{V}_b;\mathrm{del}{V}_c].

Convergence criterion

(20)\mathrm{del}{V}_{\max }=\max \{\max (\mathrm{del}V)\}.

Updating voltages in each phase

(21)v_a=V_a,

(22)v_b=V_b,

(23)v_c=V_c.

Complex power loss

(24)S_{\mathrm{br}}^{abc}=(V_p^{abc}-V_q^{abc}){(I_{\mathrm{br}}^{abc})}^{*}.

The proposed load flow algorithm is described as follows.

Step 1: Read bus data and line data for the unbalanced radial distribution system.

Step 2: Initialize the phase voltages as v_a(i)=1.0, v_b(i)=–0.5+j0.866 and v_c(i)=–0.5–j0.866.

Step 3: Calculate load currents IL_a[i], IL_b[i] and IL_c[i] using Eqs. (1)–(3) for all three phases.

Step 4: Calculate branch currents using Eqs. (7)–(9).

Step 5: Calculate the voltage drops in all three phases using Eqs. (10)–(12).

Step 6: After calculating voltage drops, find receiving end voltages in the forward direction using Eqs. (13)–(15).

Step 7: Find delV using Eqs. (16–19). Update the voltages in all three phases as shown in Eqs. (21)–(23).

Step 8: Find error in voltage i.e.delV_max. If it is less than 0.00001, the load flow is converged, otherwise go to Step 3.

Step 9: Once load flow is converged, bus voltages and branch currents are known. Then find complex power loss using Eq. (24).

Step 10: Stop.

Proposed voltage stability index for optimal D-STATCOM placement

The voltage stability index proposed in Ref. [³⁰] is modified in this paper for optimal allocation of D-STATCOM. The equivalent circuit model of RDS is illustrated in Fig. 3. The mathematical model of the proposed stability index is given below.

The branch current can be calculated using Eq. (25)

(25)I_{\mathrm{12}}={\left[{\displaystyle \frac{P_{\mathrm{2}}+j{Q}_{\mathrm{2}}}{V_{\mathrm{2}}\angle \delta }}\right]}^{*}.

The receiving end bus voltage can be written as

(26)V_2\angle \delta =V_1\angle \mathrm{0}-(R+jX)I_{\mathrm{12}}.

Substitute Eq. (25) in Eq. (26),

(27)V_{\mathrm{2}}\angle \delta =V_{\mathrm{1}}\angle \mathrm{0}-(R+jX){\left[{\displaystyle \frac{P_{\mathrm{2}}+j{Q}_{\mathrm{2}}}{V_{\mathrm{2}}\angle \delta }}\right]}^{*},

(28)V_{\mathrm{2}}^{\mathrm{2}}=V_{\mathrm{1}}{V}_{\mathrm{2}}\angle -\delta -(R+jX)(P_{\mathrm{2}}-j{Q}_{\mathrm{2}}),

(29)V_{\mathrm{2}}^{\mathrm{2}}=V_{\mathrm{1}}{V}_{\mathrm{2}}\cos \delta -j{V}_{\mathrm{1}}{V}_{\mathrm{2}}\sin \delta -(R+jX)(P_{\mathrm{2}}-j{Q}_{\mathrm{2}}),

(30)V_{\mathrm{2}}^{\mathrm{2}}+[P_{\mathrm{2}}R+Q_{\mathrm{2}}X+j(P_{\mathrm{2}}X-Q_{\mathrm{2}}R)]=V_{\mathrm{1}}{V}_{\mathrm{2}}\cos \delta -j{V}_{\mathrm{1}}{V}_{\mathrm{2}}\sin \delta .

Separate real and imaginary parts in Eq. (30),

(31)V_{\mathrm{2}}^{\mathrm{2}}+P_{\mathrm{2}}R+Q_{\mathrm{2}}X=V_{\mathrm{1}}{V}_{\mathrm{2}}\cos \delta ,

(32)P_{\mathrm{2}}X-Q_{\mathrm{2}}R=-V_{\mathrm{1}}{V}_{\mathrm{2}}\sin \delta .

Let δ≈0,

(33)V_{\mathrm{2}}^{\mathrm{2}}+P_{\mathrm{2}}R+Q_{\mathrm{2}}X=V_{\mathrm{1}}{V}_{\mathrm{2}},

(34)P_{2}X-Q_{2}R=\mathrm{0},

(35)X={\displaystyle \frac{Q_{\mathrm{2}}R}{P_{\mathrm{2}}}}.

Put the value of X in Eq. (31),

(36)V_{\mathrm{2}}^{\mathrm{2}}+P_{\mathrm{2}}R+Q_{\mathrm{2}}{\displaystyle \frac{Q_{\mathrm{2}}R}{P_{\mathrm{2}}}}=V_{\mathrm{1}}{V}_{\mathrm{2}},

(37)V_{\mathrm{2}}^{\mathrm{2}}-V_{\mathrm{2}}{V}_{\mathrm{1}}+\left({\displaystyle \frac{Q_{\mathrm{2}}^{\mathrm{2}}}{P_{\mathrm{2}}}}+P_{\mathrm{2}}\right)R=\mathrm{0.}

For stable bus voltages, b²–4ac≥0. It results in a new stability index given by Eq. (39),

(38)V_{\mathrm{1}}^{\mathrm{2}}-\mathrm{4}\left({\displaystyle \frac{Q_{\mathrm{2}}^{\mathrm{2}}}{P_{\mathrm{2}}}}+P_{\mathrm{2}}\right)R\ge \mathrm{0},

(39)\mathrm{VSI}={\displaystyle \frac{\mathrm{4}R}{V_{\mathrm{1}}^{\mathrm{2}}}}\left({\displaystyle \frac{Q_{\mathrm{2}}^{\mathrm{2}}}{P_{\mathrm{2}}}}+P_{\mathrm{2}}\right)\le \mathrm{1.}

Under normal operating conditions, the VSI value should be less than unity. If the value of VSI is closer to zero, the system will be more stable. If the value of VSI is high, the system is vulnerable to stability. The bus with a high VSI value is more sensitive and it is selected for optimal D-STATCOM placement. From Fig. 4, it can be observed that VSI is maximum in 17th branch i.e., 15th bus for the 25-bus UBRDS which is selected as optimal bus for D-STATCOM placement.

Load modelling and cost function

1) Load model [³¹]

The realistic load model is mathematically represented by Eqs. (40) and (41). In this paper, summer and winter loads are considered for the analysis.

(40)P=P_o{\left({\displaystyle \frac{V}{V_o}}\right)}^{n_p},

(41)Q=Q_o{\left({\displaystyle \frac{V}{V_o}}\right)}^{n_q}.

The exponent values and load compositions for each load type are given in Ref. [³¹].

2) Load growth [³¹]

(42){\mathrm{Load}}_i=\mathrm{Load}\times {(1+r)}^m,

where r is the annual growth rate and m is the plan period up to which the feeder can take the load.

In this paper, r=10% and m=7.

3) Cost of energy loss (CEL) [³⁰]

(43)\mathrm{CEL}(\$)=(\mathrm{Total\; real\; power\; loss})\times (E_{c}T),

where E_c is the energy rate/($∙kWh^–1) and T is the time duration/h.

In this paper, E_c = 0.06 $/kWh and T=8760 h.

4) Cost of D-STATCOM [¹⁴]

(44){\mathrm{Cost}}_{D-\mathrm{STATCOM}}(\$)=\mathrm{Investment}\_{\mathrm{cost}}_{D-\mathrm{STATCOM}}{\displaystyle \frac{{[\mathrm{1}+B]}^{n\mathrm{DST}}B}{{[\mathrm{1}+B]}^{n\mathrm{DST}}-\mathrm{1}}},

where nDST is the longevity of DSTATCOM and B is the asset rate of return.

In this paper, Investment_cost=50 $/kvar, B=0.1, and nDST=30 years.

5) Savings in cost of energy loss/$

\begin{array}{l}\mathrm{Savings\; in\; cost\; of\; energy\; loss}(\$)=\mathrm{CEL}(\$)\mathrm{in\; base\; case}-\mathrm{CEL}(\$)\mathrm{with\; D}-\mathrm{STATCOM}\\ \mathrm{Net\; saving}(\$)=\mathrm{CEL}(\$)\mathrm{in\; basecase}-(\mathrm{CEL}(\$)\mathrm{with\; D}-\mathrm{STATCOM}+\mathrm{Cost\; of\; D}-\mathrm{STATCOM}(\$))\end{array}

Optimal D-STATCOM size using variation algorithm

The procedure of finding optimal size of D-STATCOM is explained in the flowchart given in Fig. 5.

The total cost is the summation of CEL after placement of D-STATCOM and the cost of D-STATCOM. The size of D-STATCOM is obtained for both test system for rated load and with the load growth subjected to minimization of total cost, as displayed in Figs. 6 and 7.

Results and discussion

In this paper, VSI approach is applied for optimal location of D-STATCOM. The realistic voltage dependent large industrial motor load and the impact of load growth are considered. Further, light, medium and high loading scenarios are also taken into consideration. Load multiplication factors are taken as 0.5, 1.0 and 1.6 for light, medium and high loading scenarios respectively. The results are obtained in terms of voltage profile, power losses, cost of energy losses, and annual energy savings with and without installation of D-STATCOM on standard 25-bus UBRDS [³²] using Matlab software version 7.8, 2009 [³³]. The results have been obtained for the following four cases:

Case 1: Light load (half of the given rated load)

Case 2: Medium load (at rated load)

Case 3: High load (60% increase of the rated load)

Case 4: Annual load growth of 10% for 7 years

Case 1

In light load operation, the power demand in each phase is 643.98+j475.2, 649.98+j480.6, and 649.98+j480. The total power losses in the system are 50.794+j56.714. The power taken from the substation in each phase is 826.3512 kVA, 834.1653 kVA, and 830.7835 kVA. The minimum bus voltages (p.u) are found to be 0.95861, 0.95848, and 0.96314, while the maximum voltage regulations (%) are found to be 4.139, 4.152, and 3.686. Due to the system power losses, the cost of energy losses to be paid by the DNOs is $26698.

As described in Section 4, D-STATCOM is placed at the 15th bus. The D-STATCOM rating of 150 kvar is installed as per the cost analysis mentioned in Section 6. After installation of D-STATCOM, 150 kvar reactive power is locally supplied in each phase, thereby, the powers taken from the substation are reduced to 658.502+j341.416, 665.279+j345.439, and 661.509+j345.606. The total power loss in the system is reduced to 41.35+j46.661. The minimum bus voltages (p.u) are improved to 0.96491, 0.96417, and 0.96913 while the maximum voltage regulation (%) is reduced to 3.509, 3.583, and 3.087. The annual cost of energy savings obtained by DNO due to the reduction of power losses is $5129.

Case 2

In medium load operation, the power demand in each phase is 1073.3+j792, 1083.3+j801 and 1083.3+j800. The total power losses in the system are 146.442+j163.279. The power taken from the substation in each phase is 1409.105 kVA, 1421.648 kVA, and 1412.124 kVA. The minimum bus voltages (p.u) are found to be 0.92951, 0.92944, and 0.93747 while the maximum voltage regulations (%) are found to be 7.049, 7.056, and 6.253. Due to the system power losses, the cost of energy losses to be paid by the DNOs is $76969.

As described in Section 4, D-STATCOM is placed at the 15th bus. The D-STATCOM rating of 300 kvar is installed as per the cost analysis mentioned in Section 6. After installation of D-STATCOM, 300 kvar reactive power is locally supplied in each phase, thereby, powers taken from the substation are reduced to 1114.541+j537.809, 1126.599+j542.89, and 1115.812+j543.659. The total power losses in the system are reduced to 117.052+j131.358. The minimum bus voltages (p.u) are improved to 0.94229, 0.94094, and 0.94959 while the maximum voltage regulation (%) is reduced to 5.771, 5.906, and 5.041. The annual cost of energy savings obtained by DNO due to the reduction of power losses is $16199.

Case 3

In high load operation, the power demand in each phase is 1717.3+j1267.2, 1733.3+j1281.6, and 1733.3+j1280. The total power losses in the system are 398.42+j443.2. The power taken from the substation in each phase is 2339.844 kVA, 2357.952 kVA, and 2331.657 kVA. The minimum bus voltages (p.u) are found to be 0.88316, 0.88342, and 0.89706 while the maximum voltage regulations (%) are found to be 11.684, 11.658, and 10.294. Due to the system power losses, the cost of energy losses to be paid by the DNOs is $209410.

As described in Section 4, D-STATCOM is placed at the 15th bus. The D-STATCOM rating of 550 kvar is installed as per the cost analysis mentioned in Section 6. After installation of D-STATCOM, 550 kVA reactive power is locally supplied in each phase, thereby, powers taken from the substation are reduced to 1829.04+j840.41, 1850.01+j844.22, and 1820.281+j845.57. The total power losses in the system are reduced to 315.431+j351.4. The minimum bus voltages (p.u) are improved to 0.90709, 0.90487, and 0.91968 while the maximum voltage regulation (%) is reduced to 9.291, 9.513, and 8.032. The annual cost of energy savings obtained by DNO due to the reduction of power losses is $46940.

Case 4

In load growth operation, the power demand in each phase is 2091.6+j1543.4, 2111+j1560.9, and 2111+j1559. The total power losses in the system are 614.47+j682.51. The power taken from the substation in each phase is 2917.575 kVA, 2937.358 kVA, and 2895.953 kVA. The minimum bus voltages (p.u) are found to be 0.8544, 0.85504, and 0.87234 while the maximum voltage regulations (%) are found to be 14.56, 14.496, and 12.766. Due to the system power losses, the cost of energy losses to be paid by the DNOs is $322970.

As described in Section 4, D-STATCOM is placed at the 15th bus. The D-STATCOM rating of 700 kvar is installed as per the cost analysis mentioned in Section 6. After installation of D-STATCOM, 700 kvar reactive power is locally supplied in each phase, thereby, powers taken from the substation are reduced to 2264.19+j1033.04, 2290.67+j1034.19, and 2244.12+j1034.99. The total power losses in the system are reduced to 485.38+j538.92. The minimum bus voltages (p.u) are improved to 0.88526, 0.88264, and 0.90148 while the maximum voltage regulation (%) is reduced to 11.474, 11.736, and 9.852. The annual cost of energy savings obtained by DNO due to the reduction of power losses is $74340.

The voltage profiles with and without installation of D-STATCOM for light, medium and high loading scenarios including load growth are depicted in Figs.8–11 and the summaries of results after installation of D-STATCOM for all cases are given in Tables 1–4.

It can be observed that the voltage profile of each phase is improved significantly after installation of D-STATCOM for all the cases. In addition, there is a significant reduction in losses which, in turn, saves energy. The percentage loss reduction are obtained after installation of D-STATCOM for each case as demonstrated in Fig.12.

Conclusions

In this paper, unbalanced radial distribution system analysis was conducted with D-STATCOM placement. A new index was proposed for finding the location for D-STATCOM. The results were obtained for various loading conditions. Based on the analysis, the following conclusions are made.

With D-STATCOM, there is a considerable decrease in the real and reactive power loss in each phase for all the cases. With D-STATCOM, there is a significant improvement in voltage profile and, thereby, enhancement in voltage stability margin for all the cases. With installation of D-STATCOM, there is a considerable net cost of energy savings annually.

The analysis was conducted on a large industrial load model with light, medium and high loading scenarios. Further, the impact of load growth was also considered for better planning of the system. The annual savings obtained with D-STATCOM without and with load growth were observed to be higher. Hence, this study can help the DNOs to plan a better distribution system with optimal reactive power planning.

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