In this paper, a new methodology for the optimal investment in distributed generation is presented, based on an optimal allocation of combined DG and capacitor units to alleviate network voltage constraints and reduce the interconnection cost of renewable generation integration in public medium voltage distribution networks. An analytical optimization method is developed, with the inclusion of practical considerations that are typically neglected in developed works: network topology reconfiguration and the geographical data of the generation land-use and network infrastructure. Powerful results concluded from a sensitivity analysis study of the most impacted parts of the network by the variation of active and reactive power injection under network topology reconfiguration are used as a basis for capacitor units placement. A case study, with two meshed IEEE 15-bus feeders and a new DG to connect, geographical dispersed, are used to simulate the performance of the proposed approach. A cost evaluation of the obtained results proves the effectiveness of the proposed approach to reduce the required charges for connecting new renewable generation units in medium voltage distribution system.
Several optimization efforts had been presented in literature with a main aim of maximizing the benefits expected from connecting DGs to electrical networks, by optimizing their location with a defined specific capacity [
To solve their optimization problem, authors had developed several methods and approaches, which can be classified in four principal categories: analysis approaches [
In this paper, a novel objective function is introduced in the research field area of the integration of distributed generation in power systems, with the development of a powerful optimization method for identifying the optimal combined solution of underground cables and/or overhead lines to lay and capacitor units to install, for reducing the interconnection charges of the generation unit.
Several investment models were presented in literature, investment costs, substation expansion investment cost, operation and maintenance costs, energy losses cost, and the cost of the power purchased from the transmission system. In [
The proposed interconnection cost reduction methodology is based on the assumption that the cost of capacitor bank is lower compared to the costs required for underground MV cables lying and overhead MV lines development. The optimal allocation of the combined renewable generation and capacitor banks is based on powerful observations concluded from a sensitivity analysis study in Section
The main contributions of this paper are as follows: Introduction of a novel objective to the research field area of optimal allocation of distributed generation Inclusion of practical considerations that are typically neglected in already developed works Incorporating constraints related to geographical generation land use Report results that have the potential to incite researches to develop efficient efforts and encourage private investors to build renewable distributed generation by minimizing the costs of interconnecting their generation units in public networks The presentation of a powerful tool that could be used directly by distribution electric utilities for the orientation study, as tool able to offer more options to connect a new DG to their electrical networks
Several types of distributed generation can be distinguished, according to the technology, type of generators used, and depending on which primary energy they are exploiting; generally 2 principal types of distributed generation can be differentiating: conventional or traditional generators based on combustion engines, and nonconventional generator as follows: storage devices, electrochemical devices, and renewable device.
For connecting a new DG to a medium voltage public distribution network, as the case in Morocco, and according to the law 58–15, opening access to low and medium voltage networks and the decree No. 2-15-772 on access to the national grid of medium voltage of Morocco, the DG owner will have to address a formal request to the distribution utility.
Distribution utility conducts an orientation study to verify the feasibility of the integration of the new DG, by identifying and evaluating all possible options.
However, the efforts presented in literature, for optimally placing distributed generation, usually neglect the fact that DGs are developed in large surface area, and the choice of the DG site is influenced by several economic, climatic, and geographical conditions. Also, no work had considered the geographical data of the network infrastructure and the DG site.
To better model the problem and to develop an approach adequate for an implementation in public medium voltage distribution networks, renewable distributed generation unit is divided into three different items: DG site: the land area where the DG is developed Connection point: a point from the network cables and lines on where the DG will be connected Electrical connection: the overhead lines or underground cables to develop for linking the DG site to the connection point
In the case study presented in Figure
Single line diagram of the case study (topology structure no. 1).
In Figure
Another shortcoming in the efforts [
However, powerful observations could be concluded from an analysis study of the most impacted part of the network by the new DG with network topology reconfigurations.
Before connecting the DG unit to the distribution network, the relation between the variation in network voltage and the variation in active and reactive of the 15 buses:
After the connection of the DG at the CB1, the IEEE 15-bus network becomes a feeder with 16 buses and the relation between the total derivation of network voltage and the variation of active and reactive become
In Figures
Single line diagram of topology no. 2.
Single line diagram of topology no. 3.
Let’s now evaluate the most impacted parts of the networks by the variation of the injection active power and the variation of injected or consumed reactive of the DG. The results obtained are arranged in a descending order, and the most 7 impacted nodes are reported in Table
Voltage sensitivity analysis with respect to the variations of active and reactive power variations.
Topology no. 1 | Topology no. 2 | Topology no. 3 | ||||
---|---|---|---|---|---|---|
Voltage sensitivity with respect to active power variation | Voltage sensitivity with respect to reactive power variation | Voltage sensitivity with respect to active power variation | Voltage sensitivity with respect to reactive power variation | Voltage sensitivity with respect to active power variation | Voltage sensitivity with respect to reactive power variation | |
2 | 1,53 | 1,778 | 1,53 | 1,778 | 7,165 | 8,749 |
4 | 2,567 | 2,849 | 2,567 | 2,849 | 5,941 | 7,321 |
3 | 2,567 | 2,849 | 2,567 | 2,849 | 7,165 | 8,749 |
11 | 3,717 | 4,134 | 3,717 | 4,134 | 8,315 | 10,034 |
12 | 4,991 | 5,656 | 4,991 | 5,656 | 9,589 | 11,556 |
13 | 5,628 | 6,417 | 5,628 | 6,417 | 10,226 | 12,317 |
DG | 5,628 | 6,417 | 5,628 | 6,417 | 10,226 | 12,317 |
Table
However, the order of the most impacted nodes is still the same; the voltage of the nearest node to the connection point is the most impacted by the variation introduced by the new DG. This observation can also be concluded from the mathematical formulation of the voltage sensitivity calculation.
This powerful observation is used to identify the optimal placement of capacitor units to add (steps 6, 7, and 8 in Section
The main aim of the proposed approach is to give more options to connect a new DG to a public medium voltage distribution network and offer more chances to get the lowest way to connect a new renewable DG.
As mentioned in Section
The aim of the proposed approach is to identify the optimal allocation of capacity banks to reduce the impact of the new DG on network voltage constraints. Without the proposed approach, two kinds of solution will be presented to the DG owners: possible connection points, which satisfied all the networks constraints, and no possible connection points, in which at least one of the constraints is not satisfied. With the proposed approach possible, three kinds of solution will be presented: possible connection, which satisfied all the networks constraints, possible connection point with additional charge of installing capacitor banks and network reinforcement, which does not satisfy the constraints without additional devices, and not possible connection points, which does not satisfy the network constraints even with additional electrical equipment. The obtained results will be costing to identify the lowest option.
If the lowest option is resulting from the second category, the solution presented by electric utility to the DG owners to connect their generation unit will be presented as the development of underground cables or overhead lines from their DG site to the connection point with additional charge of acquisition, installation, and exploration of capacitor banks. The solution could also be extended for other electrical equipment: energy storage units, D-Statctom, D-FACTS, or Soft Open Points (SOPs).
To regulate the reactive power of the additional devices, several powerful local and decentralized approaches had been developed in [
Optimal DG access point in a public distribution system is to find best locations of network that gives minimum shortest distance from the DG site to that location, while satisfying certain operating constraints and distribution network actors interests. The operating constraints are voltage profile of the system, current capacity of the feeder and transformers, and the level of the total power losses, energy quality, and protection system limits. The objective function is interconnection cost reduction of a renewable distributed generation integration in public medium voltage distribution systems, which represents the cost required for the construction of overhead lines and underground cables between the generation land use and connection point in the distribution network Voltage limits: the bus voltage magnitudes are to be kept within acceptable operating limits throughout the optimization process: where Thermal limits of lines and transformers: where Power losses degradation: electric utilities are generally the entity responsible to keep the losses at lower level, to respect their interests; the new DG should not increase the total power losses of the system. The total power losses, before connecting the DG, should not be greater before the DG was connected: where Total harmonic limits: the total harmonic level at each bus should be less or equal to the maximum allowable harmonic level. Consumers connected at the MV network should not be injured too by connecting the new DG; to preserve a certain quality level at their substations, MV consumers add several devices. Any degradation in energy quality levels signify further charges for MV consumers: where Short circuit power constraint: where False tripping: where Protection blinding:
It is to notice that if the electric utility predicts to reduce the total power losses or a MV consumer needs to improve voltage profile or energy quality level, by changing the connection-point and proposing another access location, a comprise investment could be negotiated between DG owners and the other actors to cover the additional costs of connecting the new DG to the public network.
The proposed algorithms evaluate all possible connection point under all possible network topology structures; three kinds of solutions will have presented the following: possible connection, which satisfied all the networks constraints, possible connection point with additional charge of installing capacitor banks, which does not satisfy the constraints without additional devices, and not possible connection points, which does not satisfy the network constraints even with additional electrical equipment. The obtained results should be costing separately to identify the lowest option: Step 1: identify all possible connection-point “CB” to connect the new DG. Step 2: arrange the possible connection-point “CB” with their distance to the DG site. Step 3: place the new DG at the first connection-point Step 4: run the load flow analysis of the new network with an additional node on which the new DG is connected, under all possible network topology structures. And also, under different load conditions: morning/afternoon/night, summer/winter, week/days/weekend. Step 5: evaluate the voltage constraints for each topology structure, and also, under different load conditions: morning/afternoon/night, summer/winter, week days/weekend: If voltage constraints are satisfied go to step 6. If at least the voltage of one node is not within the permitted range go to step 7. Step 6: evaluate the network electrical constraints, equations ( If all constraints are satisfied the connection point is accepted as possible access point, go to step 3. If at least one of the constraints are not satisfied, the connection point is rejected, go to step 3. Step 7: place the capacitor bank at the nearest nodes to the DG connection-point. Step 8: increase the capacitor banks size. Step 9: run the load flow analysis of the new network with an additional node on which the new DG is connected, under all possible network topology structures. And also, under different load conditions: morning/afternoon/night, summer/winter, week/days/weekend. Step 10: evaluate the voltage constraints for each topology structure, and also, under different load conditions: morning/afternoon/night, summer/winter, weekdays/weekend. If voltage constraints are satisfied, go to step 9. If at least the voltage of one node is not within the permitted range, go to step 7. Step 11: evaluate the network electrical constraints, equations ( If all constraints are satisfied the connection point is accepted as possible access point with an additional investment on acquisition and installation of further capacity bank, go to step 3. If at least one of the constraints are not satisfied, the connection point is rejected, go to step 3.
The results will be presented as possible scenarios to connect the new DG. Without the proposed approach, the connection point which had not satisfied the electrical network constrains is directly rejected, but with the proposed method, some of those connection points could be accepted as possible access point of the new renewable DG but with further investment of acquisition and installation of capacity banks.
The cost of connecting DGs to an existing MV network will be reduced by this approach by choosing the shortest electrical connection and acquisition capacity banks, instead of choosing a largest electrical connection.
The cost of capacity bank is very low compared to the cost of underground MV cable lying or the development of MV overhead lines. Also, the cost of an electrical connection does not only depend on the length of cables, the nature of the geographical terrain, and the presence of constraints influence the total cost of the electrical connection.
The proposed method offers more options to connect a new DG to an existing MV network, all the solution resulting from the approach should be evaluated to calculate the total cost of connecting the new DG.
The evaluation of all network topology structures needs high computational effort, which impacts the time application; however, this limitation is not necessarily critical in DG placement applications.
The flow chart of the possible algorithm is given in Figure
Flow chart of the proposed approach.
The proposed analytical approach had been applied to the electrical system, presented in Figure
Load data and line data of the two meshed feeders A and B (feeder A and feeder B are identical).
Sending node (A) | Receiving node (A) | Sending node (B) | Receiving node (A) | kVA | kVAr | ||
---|---|---|---|---|---|---|---|
1 | 2 | 1 | 2 | 1.353 | 1.323 | 44.1 | 44.99 |
2 | 3 | 2 | 3 | 1.170 | 1.144 | 20.1 | 11.44 |
3 | 4 | 3 | 4 | 0.841 | 0.822 | 40 | 142.8 |
4 | 5 | 4 | 5 | 1.523 | 1.027 | 44.1 | 44.99 |
2 | 9 | 2 | 9 | 2.013 | 1.327 | 10 | 4.82 |
9 | 10 | 9 | 10 | 1.686 | 1.137 | 10 | 4.82 |
2 | 6 | 2 | 6 | 2.557 | 1.724 | 20 | 21.41 |
6 | 7 | 6 | 7 | 1.088 | 0.734 | 20 | 21.44 |
6 | 8 | 6 | 8 | 1.251 | 0.844 | 14.1 | 9 |
3 | 11 | 3 | 11 | 1.795 | 1.211 | 30 | 10.82 |
11 | 12 | 11 | 12 | 2.448 | 1.651 | 20 | 11.41 |
12 | 13 | 12 | 13 | 2.013 | 1.357 | 44.1 | 44.99 |
4 | 14 | 4 | 14 | 2.230 | 1.504 | 70 | 71.41 |
4 | 15 | 4 | 15 | 1.970 | 0.807 | 40 | 42.82 |
Distance between possible connection point and DG site.
CB1 | CB2 | CB3 | CB4 | CB5 | CB6 | CB7 |
---|---|---|---|---|---|---|
1270 m | 2404 m | 2446 m | 2630 m | 2815 m | 3007 m | 3085 m |
Firstly, the seven possible connection points CBi are tested considering all possible topology structure of the two feeders, obtained by changing the sectionalize switches and tie switches of all system nodes.
The results of the maximum and the minimum voltage magnitude for the three different topology structures are provided in Table
Evaluation of the seven connection points with respect to the voltage profile under three different topology structures.
Before DG | CB1 | CB2 | CB3 | CB4 | CB5 | CB6 | CB7 | ||
---|---|---|---|---|---|---|---|---|---|
Structure 1 | 0.98 | 1.06 | 1.05 | 1.04 | 1.05 | 1.03 | 1.03 | 1.00 | |
0.97 | 1.00 | 1.01 | 1.00 | 1.01 | 1.01 | 0.99 | 0.99 | ||
Structure 2 | 0.97 | 1.05 | 1.03 | 1.01 | 1.03 | 1.04 | 1.08 | 1.06 | |
0.92 | 0.96 | 0.97 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | ||
Structure 3 | 0.97 | 1.06 | 1.01 | 1.00 | 1.00 | 1.02 | 0.99 | ||
0.92 | 0.99 | 0.99 | 0.99 | 0.98 | 0.96 | 0.94 | 0.94 |
The results obtained in Table
By applying the proposed approach, the optimal allocation of reactive power devices obtained are two capacitors banks of 100 kVAr at nodes “12A” and “13A.” The system performance after the connection of the new DG at CB1 and the installation of the two capacitor banks at the optimal locations is given in Table
Voltage profile before the connection of the new DG, after the connection at CB1, with and without the proposed method.
Before the connection of the new DG at CB1 | After the connection of the DG at CB1 | |||
---|---|---|---|---|
Without the proposed method | With the application of the proposed method | |||
Structure 1 | 0.98 | 1.06 | 1.05 | |
0.97 | 1.00 | 1.01 | ||
Structure 2 | 0.97 | 1.05 | 1.03 | |
0.92 | 0.96 | 0.97 | ||
Structure 3 | 0.97 | 1.06 | ||
0.92 | 0.99 | 0.99 |
Without the application of the proposed method, the nearest possible access point for the new DG is CB2; however, with the introducing of the proposed approach, DG owners will be able to connect their DG unit at CB1, which presents half the length of cables needed to lay to reach the network, but with additional charges of installing and exploring two capacitors banks of 100 kVAr.
An estimation of connecting the new DG at CB1 with 2 additional capacitor banks of 100 kVAr is 183060.00 Moroccan Dirham, including taxes (19262.49 US dollar), needed to develop and install 10 electric MV cement poles of 12 meter/300 daN, 4 electric poles of 12 meter/500 daN, 14 electrical cross arms, 54 composite insulators, 1 disconnect switch, 3810 meters of conductor’s aluminum alloy (Almelec) with a section 34.4 mm2, and 2 capacitors banks of 100 kVAr.
Without the proposed solution, the new DG will be connected at CB2, with a cost of 283545.00 Moroccan Dirham, including taxes (29836.02 US dollar) to develop an overhead line of 20 MV electric cement poles of 12 meter/300 daN, 7 electric poles of 12 meter/500 daN, 27 electrical cross arms, 102 composite insulators, 1 disconnect switch, and 7212 meters of conductor’s aluminum alloy (Almelec) with a section 34.4 mm2, which clearly confirm the ability of the proposed approach to reduce the cost of connecting a renewable generation unit to a medium voltage distribution network.
This paper presented an analytical approach for optimally allocating renewable distribution generations and capacitor banks, with a main aim of minimizing the cost of connecting a new renewable DG unit to public medium voltage distribution systems, considering practical constraints of network topology reconfigurations and the presence of several actors with different interests in a competitive electrical market.
Simulation results obtained from a two meshed feeders showed that the proposed method is able to minimize the total length of electrical cables and lines needed to connect a new generation unit to a public distribution network while satisfying actors interests and network constraints.
The approach presented in this paper was developed based on an analytical approach; several heuristics and numerical methods are more robust and more efficient and could be used for future improvement. Further constraints could be adopted as time varying of load demand and renewable generation and also the consideration of load growth, if multiple years are considered and an optimal DG placement along a planning horizon is searched. Further actuators devices could also be added for further improvement as energy storage units, D-Statctom, D-FACTS, or Soft Open Points (SOPs).
The code MATLAB developed and used to perform the proposed method is available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.