A Two-Timescale Metaheuristic Approach for Coordinated Renewable Integration and Voltage Regulation in Distribution Networks

Environmental concerns are a main reason for this, so power systems today are adding renewable energy resources (RERs) that are spread out, like photovoltaic (PV) panels and wind energy. The high resistance impedance ratio R/X of these distribution feeders, along with changes in renewable output or sudden load shifts, such as electric vehicle (EV) charging, can cause voltage to swing quickly. This rapid change causes on-load tap changing transformers (OLTC) and capacitors to switch often, which shortens their life span. Various voltage regulation approaches have been suggested to manage this, depending on the type of control used, which can be grouped into decentralized, centralized, and distributed control [1].

Decentralized control, which is the simplest and most common method, determines voltages based only on local voltage data [2, 3]. But it is not the best, especially as distributed energy resources (DERs) near their control limits [4, 5]. Centralized control uses all data from the system to optimize reactive power flow [6, 7]. Still, limited communication infrastructure and limited scalability in active distribution systems hinder this method [8].

Distributed voltage control is a way to balance decentralized and central control can get info from nodes nearby [9, 10]. Still, many today use offline methods they need a while to finish and then change the control signals for this reason, online algorithms are needed they can change the control signals on the fly based on measured data [11]. Some online distributed algorithms are out there [12, 13], but they only look at DERs they don’t work with the older regulators like OLTC [14]. Without a proper plan, the control errors may significantly affect system stability, it is why coordinated controls are so important [15].

Volt/VAR control (VVC) is generally split into local and centralized options [16]. Local VVC works by reading voltage levels nearby, making it quick and easy but not able to get full system control. On the other hand, centralized control uses global data like network info and load/RES predictions to have many devices work together for better voltage control [17]. Because they are mechanical and react slowly, traditional VVC devices like capacitor banks (CBs) and OLTCs run the risk of wearing out with continuous operation [12-15]. Because power electronics-based solutions, such as D-STATCOMs and static voltage compensators (SVCs) provide significantly faster response times and greater reactive power injection flexibility, they are better suited to dynamic grid conditions.

This work presents a way to control the best tap positions in a transformer by using a modified multi-objective cuckoo search algorithm (CSA) method. Main points include the best real-time solar power and load distribution for the hours of the day and the 15-minute periods in a day, the control of voltage in a utility system and the coordination of voltage, modeling for the setup DGs grids, and how to reduce losses. The proposed algorithm optimally locates, sizes, and coordinates DGs and D-STATCOMs with tap settings, validated through performance evaluation on the IEEE 33-bus assessment system. The overall framework of the voltage regulation planning process is presented in detail in Figure 1 below.

24-1.png

Figure 1. Refinement perception in voltage regulation arrangement

Consistent function and dependable provision remain the foremost goals of any power system. The literature highlights the standing of adequate directives in grid-connected RERs structures to enhance the voltage contour and ensure system steadiness through minimal voltage controller devices [26]. Figure 2 illustrates the drift of info required towards addressing the optimization delinquent. The subsequent subcategories detail the multifunctional optimization method suggested in this study. The OLTC, illustrated in Figure 1, stands a mechanism utilized towards control voltage by altering a twisting to meet operational requirements whereas the transformer is energized and underloaded. The oil reservoir of the transformer’s tap modifier apparatus has linking facts for adjustable shot proportions that could be certain in separate increments. The transformer’s downriver bus voltage stays improved by picking the optimal beat location, which involves 2 to 10 seconds to adjust the beat setting. The default tap settings of the OLTC are generally uniform crosswise different constructers devices, such that raising the tap position leads to an increase in the quantity of primary turns, subsequently boosting the secondary voltage of the transformer and; consequently, the voltage downstream. Contrastingly, the downstream voltage is lowered by reducing the tap area. If bus voltages endure inside admissible operating confines, the generators, transformers and reactive sources of power in the arrangement can placate the kvar load prerequisite. Yet, as soon as the bus is profoundly laden, the bus voltage might surpass the acceptable voltage pose boundary, compelling the tap to recurrently alteration its location to maintain relentless bus voltage echelons. The voltage on the operative turn proportion of the OLTC could stay articulated as in Eq. (1), by the distinct transformer taps operational perimeter. Wherever $V_{L B}^{t a p}$ and $V_{U B}^{ {tap}}$ stay the inferior and superior voltage limitations, $\mathrm{V}_{\mathrm{i}}^{{set}}$ stay the anticipated voltage level.

$\mathrm{V}_{\text {Tap}, \mathrm{i}}(\mathrm{t})= \begin{cases}\mathrm{V}_{\text {Tap,i}}(\mathrm{t }) \text { if } \mathrm{V}_{\mathrm{LB}} \leq \mathrm{V}_{\mathrm{i}}^{\text {set }}(\mathrm{t}) \leq \mathrm{V}_{\mathrm{LB}} \\ 1+\operatorname{Tap}_{\text {pos}, \mathrm{i}}(\mathrm{t}) \Delta \mathrm{V}_{\text {step}} \text { if } \mathrm{V}_{\mathrm{i}}^{\text {set }}(\mathrm{t})<\mathrm{V}_{\mathrm{LB}} \\ 1-\operatorname{Tap}_{\text {pos}, \mathrm{i}}(\mathrm{t}) \Delta \mathrm{V}_{\text {step}} \text { if } \mathrm{V}_{\mathrm{i}}^{\text {set}}(\mathrm{t})>\mathrm{V}_{\mathrm{LB}}\end{cases}$                  (1)

Let it be assumed that “N” is the entire quantity of buses in a power grid, then “T” embodies the overall period, although ∆t is the time step. The power equilibrium calculation at time “t” in each bus could be inscribed for instance,

$\sum_{\mathrm{i}=1}^{\mathrm{N}} \mathrm{P}_{\mathrm{DG}_{\mathrm{i}}}(\mathrm{t})+\sum_{\mathrm{i}=1}^{\mathrm{N}} \mathrm{P}_{\mathrm{G}_{\mathrm{i}}}(\mathrm{t})=\sum_{\mathrm{i}=1}^{\mathrm{N}} \mathrm{P}_{\mathrm{Di}}(\mathrm{t})+\sum_{\mathrm{i}=1}^{\mathrm{N}} \sum_{\mathrm{j}=1}^{\mathrm{N}} \mathrm{P}_{\mathrm{ij}}(\mathrm{t})$           (2)

The distribution load flow (DLF) technique in Eq. (8) is adapted to yield DGs group into interpretation as adverse loads; henceforth, it could be inscribed for example in Eq. (11). Here, the dynamic loads are rationalized in apiece reiteration of the power stream

$\left(\mathrm{P}-\mathrm{P}_{\mathrm{DG}_{\mathrm{i}}}\right)-\mathrm{f}_{\mathrm{P}}(\mathrm{V}, \delta)=0$             (3)

The time-varying load archetypal discussed in this research combines residential, industrial and commercial loads. Hourly and 15-minute interval load variations for these models are considered in the load stream study. Real and reactive power heaps are modelled according to the equations. 

$P=P_\circ\left[\propto\left(\frac{V}{V_\circ}\right)^{n_{p r}}+\beta\left(\frac{V}{V_\circ}\right)^{n_p}+\gamma\left(\frac{V}{V_\circ}\right)^{n_{p_i}}\right]$            (4)

$\mathrm{Q}=\mathrm{Q}_{\circ}\left[\propto\left(\frac{\mathrm{V}}{\mathrm{V}_\circ}\right)^{\mathrm{n}_{\mathrm{qr}}}+\beta\left(\frac{\mathrm{V}}{\mathrm{V}_\circ}\right)^{\mathrm{n}_{\mathrm{qc}}}+\gamma\left(\frac{\mathrm{V}}{\mathrm{V}_\circ}\right)^{\mathrm{n}_{\mathrm{q}_{\mathrm{i}}}}\right]$                (5) 

The projected optimization method's multi-objective function in Eq. (6) seeks to maximize DGs and reduce the swapping sequences of the OLTC. Simultaneously, keeping the voltage levels inside ordinary operational restrictions to ensure power steadiness. Taking this into account, processes inspired by nature are utilized to address the optimization issue. It is important to mention that in this study, the cuckoo search algorithms have been enhanced to incorporate conditional values, referred to as the proportion of swelling voltage eccentricity to the extreme functioning boundary of OLTC.

$\begin{array}{r}\text { Minimize } \mathrm{MF}=\sum_{\mathrm{t}}^{\mathrm{T}}\left(\mathrm{P}_{\mathrm{TL}}(\mathrm{t})+\sum_{\mathrm{i}}^{\mathrm{G}} \operatorname{Tap}_{\text {tpos }, \mathrm{i}}(\mathrm{t})\right. \left.+\sum_{\mathrm{i}}^{\mathrm{N}}\left(\mathrm{V}_{\mathrm{i}}(\mathrm{t})-\mathrm{V}_{\mathrm{Ref}}\right)\right)\end{array}$             (6)

where, $\operatorname{P_{T L}}$, $\operatorname{Tap}_{\text {tpos}, i}$, $\left(\text{V}_\text{i(t)}-\text{V}_\text{Ref}\right)$ are overall power fatalities, entire tap changed location “recognized as the overall number of substituting sequences” and voltage aberrations crossways buses.

24-2.png

Figure 2. Overall methodology flowchart of cuckoo search algorithm (CSA)

3.1 Radial load flow

Orthodox Newton-Raphson methods and fast-decoupled load stream stand generally employed for resolving transmission systems. These approaches rely on resolving the Jacobian matrix or using the Z-matrix method. Toward resolve load stream approaches grounded on the Jacobian matrix, the contrary of the Jacobian matrix necessity be. Yet, in nearly belongings, the Jacobian matrix turns into singular due to the high resistance to reactance (R/X) percentage of distribution lines. Further, Z-matrix grounded load stream procedures require a set of calculations comparative to the sum of buses, thus demanding supplementary properties and time. This requirement led to the change of radial load flow (RLF) procedures.

The Teng technique is known as a direct approach for resolving centrifugal and faintly mesh systems. This approach is focused on building two derivative matrices: branch injection to branch current (BIBC), and branch current to bus voltage (BCBV). For circulation grids, the correspondent current inoculation constructed model structures as more practical. For bus i, the composite load $s_i$ is articulated by

$s_i=\left(P_i+j Q_i\right) i=1,2 \ldots \ldots . N$               (7)

And the conforming comparable current inoculation at the $n-t h$ reiteration of explanation is

$I_i^n=I_i^r\left(V_i^n\right)+j I_i^i\left(V_i^n\right)=\left(\frac{P_i+j Q_i}{V_i^n}\right)$            (8)

where, $V_i^n$ and $I_i^n$ are the bus voltage and equitant bus current inoculation at $n-t h$ reiteration, and $I_i^r I_i^i$ are the real and imaginary portions of the conforming current inoculation of bus at the $n$ - th reiteration, correspondingly.

The affiliation among the bus current inoculations and subdivision currents can be expressed as

$[B]=[B I B C][I]$               (9)

where, BIBC is the bus-injection to branch-current (BIBC) matrix. The relentless BIBC matrix is a superior deltoid matrix and comprises principles of 0 and 1 solitary.

Additionally, the affiliation among branch currents and bus voltages can be written as

$[\Delta V]=[B C B V][B]$           (10)

where, BCBV is the branch-current to bus-voltage (BCBV) matrix.

From Eq. (9), Eq. (10) can be inscribed as

$[\Delta V]=[B C B V][B I B C][I]$           (11)

During backward sweep, the modification in voltage w.r.t the root node V1 is calculated consuming the calculation below.

$[\Delta V]=[D L F][I]$           (12)

And the resolution for distribution load stream could advance by explaining Eq. (8) iteratively

$I_i^n=I_i^r\left(V_i^n\right)+j I_i^i\left(V_i^n\right)=\left(\frac{P_i+j Q_i}{V_i^n}\right)$           (13a)

$\left[\Delta V^{n+1}\right]=[D L F]\left[I^n\right]$                 (13b)

$\left[\Delta V^{n+1}\right]=\left[V^o\right]+\left[\Delta V^{n+1}\right]$             (13c)

The conjunction principles of the Teng method remain specified as

$\begin{array}{r}\operatorname{Max}\left[\left|V_i^n\right|-\left|V_i^{n-1}\right|\right]<\text { tolerance where } n =1,2,3, \cdots N\end{array}$               (14)

3.2 Constraints

${Tap}_{ {pos}, i}^{ {min}} \leq {Tap}_{{pos}, i}(t) \leq {Tap}_{{pos, i}}^{{max}}$            (15)

$V_i^{\min } \leq V_i(t) \leq V_i^{\max }$            (16)

$Bus_2 \leq{Location}_{D G, { Dst }, B t} \leq {Bus}_N$           (17)

$P_{DG.Bt,k}^{min} \leq P_{D G, k}(t) \leq P_{D G, B t, k}^{\max }, k=1,2, \ldots, m$                (18)

$\sum_{d=1}^{N D G} P D G \leq \sum_{i=1}^{n d} P_{d i}(i)$           (19)

$Q_{{D s t, k}}^{\min } \leq P_{D s t, k}(t) \leq P_{D s t, k}^{\max}, k=1,2, \ldots, m$          (20)

$\sum_{d=1}^{N D S t} Q D s t \leq \sum_{i=1}^{n d} Q_{d i}(i)$          (21)

$C V D_{min} \leq C V D(t) \leq C V D_{max}$            (22)

$\operatorname{CVD}(t)=\sum_t^T\left(\frac{\sum_i^N\left(V_i(t)-V_{R e f}\right)_{R G}}{\sum_i^N\left(V_i(t)-V_{R e f}\right)}\right)$         (23)

3.3 Implementation of cuckoo search algorithm

This segment details how CSA is prolonged from solitary optimization towards determining multi-objective refinement for ideal provision and coordination problems of RERs addition in the power grid environment, considering practical operational requirements. Generally, the initial decree for retaining the sole refinement algorithm by one impartial function $f(x)$ is that ace egg cell is placed by respectively cuckoo and forsaken in an arbitrarily certain net (egg = nest + explanation). Aimed at multifunctional refinement, through further unity detached function $f_i(x), i \in[1,2,3, \ldots, k]$, in its place of ace egg, it is presumed that apiece cuckoo places further ace “$e g g_i, i \in[1,2,3, \ldots, k]$”, corresponding to the explanation for $f_i(x)$. In another rule, the uppermost eminence of eggs (explanation) institute in the finest nest is passed to the following peers, and so, the finest explanation for the impartial function is $\min f(x)$, whereas $\min f_i(x)$ is applied aimed at numerous impartial functions. In the past regulation of the sole impartial function, the quantity of available swarm nests is secure, whereby a swarm could determine an alien egg by a chance of “0” or “1”. If the swarm bird recognizes the cuckoo egg, whether the swarm pitches the egg or vacates the nest and sizes substitute one in a dissimilar place. Once dealing by multi-objective optimization, respective nest could be uninhibited by a level of prospect, then a novel nest by “$e g g_i, i \in[1,2,3, \ldots, k]$” is made, dependent on the variety of the eggs. The CSA tactic serves a cuckoo exploration to grip the optimization delinquent by applying dual procedures: the initial straight and works built on a levy detection, while the another is arbitrary and functions founded on the possibility for a swarm bird to notice an alien egg hip its nest. After the inhabitant’s extent constraint is secured, the superiority and stability of randomization, as well as the limited pursuit, are precisely determined by the prospect restriction. In this method, the key aim of this procedure is to substitute the deprived explanation in the nests by a novel amended resolution. This replacement process helps maintain the diversity of the population and prevents the algorithm from being trapped in local solutions during the optimization process.

$\begin{aligned} & X_i =\left[\begin{array}{c}\text {Lo}(\text {DG}, \text {Dst}, \text {Bt})_2^i, \ldots ., \text {Lo}(\text {DG}, \text {Dst}, \text {Bt})_{\text {N }}^i, \text {Pos.} T A P_1^i, \ldots, \text {Pos.} T A P_m^i \\ \text {Size} .(\text {DG}, \text {Dst})_1^i, \ldots ., \text {Size.}(\text {DG}, \text {dst})_m^i\end{array}\right], i =1,2 \ldots . N\end{aligned}$            (24)

$Lo.(D G, D s t, B t)_i=$$r o u n d\left[\operatorname{Lo}_{\text {bus} 2, d 1}^i+r\right. and \left.\times\left(\operatorname{Lo}_{\text {max}, d 1}^i-\operatorname{Lo}_{\text {bus} 2, d 1}^i\right)\right]$          (25)

$\operatorname{Pos} . T A P_i=\begin{aligned}\operatorname{round}\left[\operatorname{Pos}_{\min , d 2}^i\right. & +\operatorname{rand} \times\left(\operatorname{Pos}_{\max , d 2}^i\right. \left.\left.-\operatorname{Pos}_{\min , d 2}^i\right)\right]\end{aligned}$                (26)

$\begin{gathered} {Size.}(D G, \text {Dst}, B t)_i= {round}\left[ {Size}{ }_{\text {min,} d 3}^i+ {rand} \times \left({Size}_{ {max}, d 3}^i\right.\right. \left.\left.- {Size}_{ {min}, d 3}^i\right)\right]\end{gathered}$          (27)

The inhabitants of answers are imperiled to recurring sequences by the exploration course, and after creating novel resolutions "$x_i^{t+1}$" for a cuckoo "$i$", the Levy trip is executed. Note that afterwards respective sequence, the procedure is route to square the nests, after which respective impartial function is intended to recognize the nest by the finest aptness function to be protected as the best nest "$G^{\text {best}}$". The peers of a novel explanation (novel cuckoo eggs) via levy trip are completed consuming Eq. (24) by the extra substituted nests, founded on the excellence of novel eggs. The phase extent "$\propto$" in Eq. (28) is the remoteness among dual explanations, where this hang on the topology of space. The randomly produced number "$\eta$" is in the range of $[0,1] ; \Gamma$ is a gamma circulation function; $\Delta X_i^{\text {new}}$ is an improved worth and could regulate with Eq. (29), wherever $\eta_x$ and $\eta_y$ remain generally spread stochastic variables per usual deviation $\sigma_x(\lambda)$, as articulated in Eq. (28) and $\sigma_y(\lambda)=1$, respectively. The Levy trips occur detailed to pursuit close the answer, trailed in a large step in the extended track, signified thru dispersal aspect "$\lambda$".

$X_d^{\text {new}}=X_d^{\text {best}}+\propto\times \eta \times \Delta X_i^{\text {new}}, \quad\left\{\begin{array}{c}-1<\eta \leq 1 \\ \propto>0\end{array}\right.$            (28)

$\begin{aligned} \Delta X_i^{\text {new}}= & \left(\frac{\eta_x}{\left|\eta_y\right|^{1 / \lambda}}\right) \times\left(\frac{\sigma_x(\lambda)}{\sigma_y(\lambda)}\right) \times\left(X_i^{\text {best}}-G_i^{\text {best}}\right),\{1<\lambda \leq 3\}\end{aligned}$            (29)

Active and reactive power losses reduced significantly by integrating batteries into the system the planned arrangement achieves a maximum voltage regulation in a real-time distribution system by DGs and D-STATCOMs. Further, it can be observed that by incorporating batteries is lowest at the 7th hour than highest by the 18th hour on the day-to-day load curve. To accommodate unexpected load variations, batteries are integrated into the system to mitigate stress on voltage-regulating devices and enhance the voltage profile across all buses.

$\sigma_x(\lambda)=\left|\frac{\Gamma(1+\lambda) \sin \left(\frac{\pi \lambda}{2}\right)}{\Gamma\left(\left(\frac{1+\lambda}{2}\right) \lambda \times 2^{\left(\frac{\lambda-1}{2}\right)}\right)}\right|^{\frac{1}{\lambda}}$            (30)

$X_d^{\text {new}}=\left[\begin{array}{c}\operatorname{rand}\left[X_{d 1}^{\text {new}}\right], \operatorname{rand}\left[X_{d 2}^{\text {new}}\right], \\ \operatorname{rand}\left[X_{d 3}^{\text {new}}]\right.\end{array}\right], \operatorname{rand}\left[X_{d 4}^{\text {new }}\right]$            (31)

${Lo. DG, Dst, Bt}_{d 1}^{\text {lim}}$$= \begin{cases}2 \ {if}\ L o . R G_{d 1}<2 \\ L o_{max , d 1} \ { if }\ L o_{d 1}>L o_{\max , d 1} \\ { Lo.DG }_{d 1} {otherwise}\end{cases}$       (32)

${Pos.TAP}_{d 2}^{\text {lim}}=\left\{\begin{array}{c}\text {Pos.TAP}{ }_{\text {min}, d 2} \text { if Pos.} T A P_{d 2}<\text {Pos.} T A P_{\min , d 2} \\ \text {Pos.} T A P_{\text {max }, d 2} \text { if Pos. } T A P_{d 2}>\text { Pos. } T A P_{\text {max }, d 2} \\ \text {Pos.} \text {TAP}_{d 2} \text { otherwise }\end{array}\right.$           (33)

${Size. DG, Dst, bt }_{d 3}^{\text {lim}}=\left\{\begin{array}{c}\text {Size}_{m i n, d 3} \text { if Size}_{d 3}<\text {Size}_{m i n, d 3} \\\text { Size}_{m a x, d 3} \text { if Size}_{d 3}>\text {Size}_{m a x, d 3} \\\text { Size.} D G_{d 3} \text {otherwise}\end{array}\right.$            (34)

$\begin{aligned} & \text {Co}_{\text {rbest.} D G, \text {Dst}, \text {bt}}{ }_{d 4}^{\lim }= \left\{\begin{array}{l}\text {Co}_{\text {rbestmin,d4 }} \text { if } \text {Co}_{\text {rbest} d 4}<\text {Co}_{\text {rbest}_{\text {max}, d 4}} \\ \text {Co}_{\text {rbest} \text {max}, d 4} \text { if } \text {Co}_{\text {rbest} d 4}>\text {Co}_{\text {rbest}_{\text {max}, d 4}} \\ \text {Co}_{\text {rbest}} . \text {DG}, \text {Dst}, \text {Bt}{ }_{d 4} \text { otherwise}\end{array}\right.\end{aligned}$               (35)

In the concluding phase, where the host bird will notice the alien eggs, standing eggs will stay replaced by high-quality newly generated eggs from their current positions, as stated in Eq. (35). The novel improved rate " $\Delta X_i^{\text {new}}$" can be resolute by means of Eq. (36). The rationalized coefficient "K" is resolute grounded on the possibility of the host bird noticing the unacquainted eggs on its nest. $\eta_{p 1}$ and $\eta_{p 2}$ are the arbitrary agitation for nests sites of the $X_i^{\text {best }}$.

$\begin{aligned} & X_i^{ {new}}=X_i^{ {best}}+K \times \Delta X_i^{ {new}}, \\ & K=\left\{\begin{array}{l}1 \ { if\ rand }<P_a \\ 0, \ { otherwise }\end{array}\right.\end{aligned}$         (36)

$\Delta X_i^{\text {new}}=\eta \times\left[\eta_{p 1}\left(X_i^{\text {best}}\right)-\eta_{p 2}\left(X_i^{\text {best}}\right)\right]$          (37)

The inferior and better parameters of apiece novel explanation would content the redefined limitations in Eqs. (31)-(34). Therefore, the CSA is routed to check the nests, afterwards which respective impartial function of Eq. (6) is intended to gain the finest worth of apiece nest $X^{\text {best}}$, and the nest alike the finest aptness rate is usual near the finest nest $G^{\text {best}}$. The phases of producing novel cuckoos by Levy trip and the detection on alien eggs remain repeatedly executed till triumph the extreme iteration. Figure 2 presents the step-by-step flow chart of methodology adopted in this study based on CSA.

This study presented a two-timescale OVR scheme using a modified CSA to coordinate OLTC, DGs, D-STATCOMs, and batteries in active distribution networks. Validated on the IEEE 33-bus system with realistic hourly and 15-minute load/solar profiles, the proposed approach effectively maintains voltage within permissible limits while minimizing power losses and OLTC switching cycles.

1. The coordinated scheme-maintained bus voltages strictly within the 0.90–1.05 p.u. range across all time intervals, overcoming the limitations of OLTC-only or DG-only actions, which previously allowed voltages to drop below acceptable thresholds (e.g., 0.9091 p.u. in the base case).
2. The proposed strategy limited OLTC operations to 130 cycles per day for hourly scheduling and 365 cycles for 15-minute intervals, substantially reducing mechanical wear and extending equipment lifespan compared to uncoordinated scenarios.
3. Real and reactive power losses were significantly reduced, with the lowest CEL observed at the 7th hour (minimum load) and the highest at the 18th hour (peak load), demonstrating effective device coordination under varying conditions.
4. The framework offers distribution network operators (DNOs) a decision-support tool for real-time VVR control and is extensible to microgrids with hybrid energy sources. Future work should focus on a two-stage synchronized optimum reconfiguration context to further minimize losses and optimize OLTC operations over 24-hour variable load and solar irradiance.