GA-Based Voltage Optimization of Distribution Feeder with High-Penetration of DERs Using Megawatt-Scale Units

Abstract

In this paper, genetic algorithm (GA)-based voltage optimization of a modified IEEE-34 node distribution feeder with high penetration of distributed energy resources (DERs) is proposed using two megawatt-scale reactive power sources. Traditional voltage support units present in distribution grids are not suitable for DER-rich feeders, while voltage support using small-scale DERs present in the feeder requires considerable communication effort to reach a global solution. In this work, two megawatt-scale units are placed to improve the voltage profile across the IEEE 34-node feeder, which has been modified to include several PV units and an energy storage unit. The megawatt-scale units are optimized using GA for fast and accurate operation. The performance of the proposed scheme is verified using simulation results with a multi-platform setup where the modified IEEE-34 node feeder is modeled in OpenDSS while the GA optimization scheme is programmed in MATLAB.

1. Introduction

The landscape of the traditional distribution grid is rapidly changing with the increasing penetration of distributed energy resources (DERs) such as PVs and energy storage (ES) units. Although the addition of DER units presents several benefits, such as the reduction of fossil-fuel-based energy usage, and more potential benefits, such as improved grid resiliency, the current grid infrastructure is not equipped to deal with the stochastic nature and the bidirectional power flow in feeders associated with the high penetration of such units [1,2,3]. Therefore, more research is necessary regarding the high penetration of DER-based distribution feeders to fulfill their potential.

Traditionally, voltage support is provided in distribution grids through on-load tap-changing (OLTC) transformers and shunt capacitors. However, the tap changers and mechanical switches associated with such devices cannot respond fast enough to regulate voltage in high DER penetration distribution grids [4], making them unsuitable for such feeders. Flexible AC transmission systems (FACTS) devices scaled for the distribution grid level, referred to as distributed-FACTS (D-FACTS), can provide improved grid support. D-STATCOMs (distributed static synchronous compensators), which are the most widely utilized D-FACTS device due to their simple shunt connection, can only provide reactive power support, while grid support at the distribution level requires both active and reactive power support [5]. D-FACTS devices capable of providing both active and reactive power, e.g., UPFCs (unified power flow controllers), are less common due to their complicated architecture requiring both a shunt and series connection [6]. On the other hand, large-scale DER units can fulfill the functionalities of D-FACTS devices while being capable of providing additional support functions such as black start capability. Proper coordination is necessary between such large-scale DERs to improve performance across the feeder.

Several state-of-the-art optimization and communication techniques are present in the literature to improve distribution feeder performance with high penetration of DERs. The techniques presented can broadly be categorized as decentralized, distributed, and centralized techniques [7]. Under decentralized schemes, each DER is locally controlled and cannot guarantee feeder-level improvement. Therefore, the remaining two techniques are generally discussed in the literature. A two-stage distributed optimization process is presented in [8], where the traditional voltage support devices are optimized hourly and the individual small-scale DERs present are optimized every few minutes. The feeder is divided across several zones, and each zone is equipped with an agent that is primarily focused on optimizing the particular zone while sharing a global optimization goal with other zones. A similar zone-based distributed scheme is proposed in [9], where the optimization method is enhanced through the integration of the alternative direction multiplier method for inter-regional coordination and the branch and bound method for handling nonconvexity introduced by traditional devices. A distributed approach is also proposed in [10], where three microgrids optimize themselves independently while the distribution system operator (DSO) sets global boundaries for power exchange between the microgrids and the remaining DGs in the feeder. The distributed approaches presented in [11,12] display good performance and require less communication infrastructure than centralized options; however, an optimal global solution to the optimization problem cannot be guaranteed. Several centralized optimization techniques can also be found in the literature. In [11], a centralized energy management scheme is presented that puts emphasis on consumer electricity costs. In [12], a distributionally robust chance-constrained optimization scheme is presented that centrally optimizes the dispatch of PVs and ES units, while the DER uncertainties are modeled through a set of probability distributions. However, the work considering a centralized scheme considers simplified feeders with a small number of DER units to reduce the complexity associated with centralized techniques. Moreover, the works referenced thus far perform optimization based on traditional power system tools such as mixed integer linear programming, which require significant computation time and are not suitable for the stochastic nature of DERs. Furthermore, forecasting data and probability distributions generally used for DERs to realize real-time optimization will inevitably result in inaccuracies. One solution can be to use meta-heuristic techniques for optimization. Meta-heuristic algorithms have been extensively used for allocating resources such as shunt capacitors and DERs in distribution feeders [13,14]. In [15], a global multidimensional constrained optimization technique is used for developing energy-harvesting gravity-based devices for wind applications. The presented algorithm shows improved results over the state-of-the-art; however, its applicability to larger systems such as distribution feeders is not evident. In [16], a chaotic differential evolution algorithm is used to optimally allocate and size DERs, considering economic loss, power loss, and voltage deviation in feeders. In [17], an improved differential search algorithm is used to optimally allocate DERs in a radial distribution grid to minimize real power loss, network operational cost, and voltage profile. In [18], both DERs and D-STATCOMs are optimally sized and allocated to minimize real power loss using a genetic algorithm (GA). Similarly, DERs and capacitor banks are sized and placed using a combination of GA, DE, and the strength pareto evolutionary algorithm [19]. Power loss minimization and voltage deviation optimization are performed in [20] by controlling DERs, shunt capacitors, OLTC transformers, and flexible loads using normal distribution crossover-based non-dominated sorting GA. However, the issue regarding communication infrastructure associated with centrally controlling a large number of units still persists. Therefore, more research is necessary in real-time optimization of feeders using such techniques.

In this paper, a GA-based optimization scheme is presented to improve the voltage profile of a modified IEEE-34 node feeder with high penetration of DERs using two megawatt-scale DER units. The small-scale DER units are controlled locally independently of the proposed scheme, while the large-scale ones are centrally optimized. Central optimization allows for a globally optimal solution, and since only two units are introduced, the communication infrastructure required is minimal. On the other hand, using GA allows for fast and accurate real-time optimization.

The rest of the paper is organized as follows. In Section 2, the modified IEEE-34 node feeder is described. In Section 3, the presented optimization scheme is discussed in detail. Results are presented in Section 4 to validate the proposed scheme. Finally, conclusions are drawn in Section 5.

2. Description of the Feeder

The IEEE 34-node feeder considered for this work is shown in Figure 1. It retains all the characteristics of the existing IEEE 34-node feeder, including load values, load placements, line lengths, and the traditional voltage support devices, namely OLTC transformers and shunt capacitors [21]. However, the feeder has been modified from its traditional counterpart by adding eight PV resources and an energy storage resource [22]. The ratings of the added PVs are shown in

Table 1. PV Ratings.

PVs	Apparent Power (kVA)	MPP (kW)
844	1000	900
890	750	500
860	1250	1000
828	200	150
806	100	100
836	150	150
840	250	200
812	250	225

. The ES is rated at 250 kVA. The nominal load of the presented feeder is 2.05 MVA, which is lower than the total power of the DERs, making the feeder susceptible to the stochastic nature of the DERs. The MVA rating of the substation transformer has also been increased to account for the added resources in the feeder.

The PVs added to the feeder are actively engaging in voltage support operations using the volt-var method. However, the amount of reactive power available for voltage support is constantly changing based on the maximum power point (MPP) of the PVs. Therefore, the PVs are locally controlled and act only on the voltage profile of their local nodes.

On the other hand, the reactive power resources that are being added will act depending on the feeder-level voltage profile. The voltage profile of the feeder without the reactive power resources is shown in Figure 2. Figure 2 was generated with the power generation and consumption units at their nominal values. In other words, all the loads were operating at their rated values, and all the PVs were operating at their respective MPPs. As can be seen from Figure 2, under nominal conditions, the voltage at certain nodes can swell well beyond 1 p.u. due to DER power output. It should be noted that the traditional voltage support devices are active in this scenario, which justifies the use of additional reactive power resources. Two particular points of interest in the feeder voltage shown in Figure 2 are the ones with the lowest and highest voltage values of all the three-phase nodes, which correspond to nodes 814 and 840, respectively. Two reactive power resources are therefore added to these nodes to regulate the feeder voltage. The added resources are rated for 2 MVA. Their placements are highlighted in Figure 3. A more thorough analysis regarding the placement of reactive power resources will be considered in the future.

3. Proposed Optimization Scheme

The entire system considered in this work is divided across two platforms. The feeder model is housed in OpenDSS, while the optimization algorithm is in MATLAB. GA has been used to optimize the reactive power settings of the reactive power resources, while the infinity norm function has been employed as the optimization function.

3.1. GA Optimization

The goal of this paper is to regulate the voltage of all nodes to not violate the ±5% limit, which is required by most of the distribution grids in the world, using the minimum amount of reactive power from the large DERs. Therefore, this problem can be addressed as an optimum reactive power flow (ORPF) type, resulting in a fairly large, non-linear, multimodal optimization problem with constraints. Furthermore, the resulting objective function is non-continuous, non-differentiable, and rugous, besides possibly being non-convex. The deterministic optimization methods have difficulties dealing with this type of problem; they usually require large computational times and, when applicable, are very likely to get trapped in local minimums. On the other hand, many evolutionary algorithms have features that make them feasible for the type of problem in scope. Among the evolutionary methods, GA is a bio-inspired technique that mimics the evolution theory of Darwin by modeling natural operators such as natural selection, crossover, and mutation. Among the powerful features of GA are intrinsic parallelism and inherent global search; no requirement to explicitly model stands out. Hybrid techniques and combinations of different evolutionary methods can also be used [13], but the simplicity of GA allows for a natural expansion of this approach for more complex systems, e.g., larger feeders and simultaneous optimization of discrete (OLTCs) and continuous variables (DERs) [23,24].

The optimization function used in this work, which is the same as the fitness function (FF) of the GA scheme, is based on the infinity norm of the feeder voltage deviations as expressed in (1),

$$FF=\underset{\mathit{i}ϵ\left\{1,N\right\}}{\max }\left(\left|v_i-v_i^{*}\right|\right),$$

(1)

where, N is the total number of node voltages, v_i is the actual voltage at node i, and $v_i^{*}$ is the desired voltage at node i, which for this problem was chosen as 1 p.u. The goal is to minimize FF, which means to minimize the largest voltage deviation throughout the whole feeder. Therefore, the optimization problem can be expressed as,

$$\min \left(\underset{\mathit{i}ϵ\left\{1,N\right\}}{\max }\left(\left|v_i-v_i^{*}\right|\right)\right).$$

(2)

Based on the largest voltage deviation, the reactive power commands for the optimized units are derived in an iterative process, as will be described in the following subsection. The upper and lower bounds of the reactive powers are set at their ratings. In other words,

$${\left|Q\right|}_1^{*},{\left|Q\right|}_2^{*}\le 2\mathrm{M}\mathrm{v}\mathrm{a}\mathrm{r}.$$

(3)

The iterations will continue until the GA encounters one of its stopping criteria, ideally the maximum value of the fitness function, which will be set by the user. The maximum deviation can be set as the largest p.u. deviation in voltage that is acceptable. It should be noted that each phase of all the node voltages is considered for the fitness function.

3.2. OpenDSS MATLAB Co-Simulation Scheme

As mentioned previously, the system under consideration is divided across two platforms, as shown in Figure 3. The platforms communicate with each other using the COM interface. The modified IEEE 34-node feeder is modeled in OpenDSS. The control scheme for all the locally controlled elements, i.e., OLTC transformers, shunt capacitors, and PVs, is also modeled in OpenDSS. The added reactive power resources are modeled as energy storage devices in the OpenDSS model, while their controls are housed in MATLAB. The optimization in MATLAB is performed using the feeder node voltages. Therefore, at each GA generation, all the p.u. node voltages are sent from OpenDSS to MATLAB, while the reactive power commands are sent from MATLAB to OpenDSS. The stopping criteria for the algorithm is set at a fitness of 5%, i.e., when the largest voltage deviation across all nodes drops to less than 5%. The whole process is depicted as a schematic in Figure 4 and a flowchart in Figure 5. A schematic diagram depicting the real-time implementation of the proposed scheme is illustrated in Figure 6. The update time of the reactive power commands is set at three minutes to account for the model update process, although the GA optimization can operate much faster, as will be shown in the following section. Note that the feeder model can be executed on several simulation platforms, while OpenDSS is used for this work.

4. Results

In this section, the proposed optimization scheme is verified using use cases performed in a simulation setup. As mentioned previously, the simulation setup is built across two platforms. The modified IEEE-34 node feeder is modeled in OpenDSS, while the GA optimization scheme is housed in MATLAB. The parameters used for GA optimization are shown in

Table 2. GA Parameters.

Parameter	Value
Fitness Limit	0.04
Function Tolerance	0.001
Selection Function	Uniform
Fitness Scaling	Top
Selection Function	Uniform
Crossover	Scattered
Crossover Fraction	0.9
Mutation	Gaussian

. The parameters are chosen through trial and error to strike a balance between performance and computational time.

The voltage profile of the feeder with and without GA optimization is shown in Figure 7. This profile is generated under 50% overload and a total PV capacity of 50%. The capacity of the PVs is altered by changing the irradiation input to the units. Irradiation inputs are generated in MATLAB and sent to the OpenDSS model through the COM interface. Note that all three phases of each node are shown separately. It should also be noted that the OLTC transformers and shunt capacitors are operational in these use cases. The presence of PVs causes voltage to swell in certain nodes, while overload conditions cause voltage to sag in other nodes. As one can see from Figure 7, at one particular node (Node 20 in the figure), the voltage goes below 0.9 p.u. when the GA optimization is not enabled, while six other nodes also violate the ±5% limit. When GA optimization is enabled, after 21 iterations, the voltage across the entire feeder is spread much more uniformly with respect to the rated voltage, with the number of node voltage violations reduced to two. The reactive power setpoints generated by the optimization are −1.87 Mvar and 0.63 Mvar at nodes 888 and 814, respectively. The optimization converged in around 40.5 s, making it viable for real-time operations.

In the use case depicted in Figure 8, the feeder is operating in light load conditions with 50% of the nominal load active, while the PVs are operating in 50% overrated conditions. This causes higher voltage swells across the feeder when the optimization is not enabled. With the GA optimization enabled, a more uniform voltage profile with respect to the rated voltage can be seen in Figure 8, with the entire profile residing within the ±5% limit. A large difference in the same node voltages (nodes 84–86) can be seen in the figure with and without optimization, since these nodes correspond to Node 888, which is one of the nodes where the additional reactive power unit is added. Although the voltage deviation at that particular node is higher, the overall profile has improved. The reactive power setpoints generated in this case are −1.58 Mvar and 0.89 Mvar, while the optimization converged in about 52.8 s. It should be noted that the maximum number of stall generations was set at 20, which is why the GA results for both use cases are for 21 generations. As a future expansion of this work, the use cases will be recreated on a controller hardware-in-the-loop platform.

5. Conclusions

In this paper, a GA-based scheme has been proposed to improve the voltage profile of a high DER penetration distribution feeder by centrally optimizing two megawatt-scale units. The proposed scheme has been implemented in a modified IEEE-34 node feeder, which was converted to a high DER penetration feeder through the introduction of several PV and ES units, the total power of which was comparable to the total load of the feeder. The utilization of two large-scale units for voltage optimization instead of the existing small-scale DERs in the feeder allows for much less communication infrastructure, therefore mitigating the biggest disadvantage of central optimization while inheriting all its benefits. On the other hand, a GA-based scheme allows for quick and accurate real-time optimization of the resources. The proposed scheme has been validated through simulation scenarios carried out in an OpenDSS-MATLAB setup.