A Hierarchical Voltage Control Strategy for Distribution Networks Using Distributed Energy Storage

Abstract

This paper presents a novel hierarchical voltage control framework for distribution networks to mitigate voltage violations by coordinating distributed energy storage systems (DESSs). The framework establishes a two-layer architecture that integrates centralized optimization with distributed execution. In the upper layer, a model predictive control (MPC)-based controller computes optimal power dispatch trajectories for critical buses, effectively decoupling slow-timescale optimization from real-time adjustments. In the lower layer, a broadcast-based controller dispatches parameterized power regulation signals, enabling autonomous active power tracking by the DESS units. This hierarchical design explicitly addresses the scalability limitations of conventional centralized control and the cyber vulnerabilities of peer-to-peer distributed strategies. The effectiveness of the proposed control framework is verified on the modified IEEE 34-bus and 123-bus test feeder. The results show that the proposed method can mitigate the average voltage violation by 93.7% and show control robustness even under 60% communication loss condition.

1. Introduction

As distributed energy resources (DERs) including rooftop photovoltaics (PVs) and electric vehicles (EVs) become increasingly integrated into power systems, contemporary distribution networks now face unprecedented hurdles in maintaining stable voltage regulation [1,2]. The intermittent output of DERs, combined with abrupt load changes and reverse power flows, often leads to voltage deviations exceeding the permissible limits (e.g., ±5% of the nominal voltage in IEEE standards [3]). Conventional voltage regulation apparatuses, including on-load tap changers (OLTCs) and switched capacitors, face inherent limitations in modern distribution networks, including delayed response times, coarse regulation granularity, and excessive communication overhead in large-scale deployments [4]. As a result, there is an urgent need for advanced voltage control strategies that can leverage flexible resources like distributed energy storage systems (DESSs) to maintain voltage stability in distribution networks [5].

Recently, there have been several model predictive control (MPC)-based methodologies proposed for voltage control in renewables-dominated networks [6,7,8]. For instance, in [9], an MPC-based centralized controller is proposed for real-time voltage coordination. In [10,11], MPC-based voltage control methods are developed to regulate the voltage with different controllable resources. In [12], an optimal real-time voltage regulation is proposed to reduce the impact of PVs. However, these approaches are implemented in a centralized manner, which struggles with inadequate scalability when integrating the ever-growing proliferation of DERs into modern distribution networks [4,13].

To deal with this issue, many distributed voltage control methods are proposed in recent literature [14]. For instance, in [15,16], distributed model predictive control (DMPC) approaches are proposed based on the voltage sensitivity method. In [17], a distributed voltage control framework is presented for distribution networks embedded with distributed generators, which is efficiently resolved through the alternating direction method of multipliers (ADMMs). In [18], a modified dynamic consensus-based algorithm to orchestrate real-time volt-var control of distributed inverter. In [19,20], distributed voltage controllers derived from deep reinforcement learning are proposed to mitigate voltage violations through adaptive agent interactions. In [21,22], fully distributed real-time voltage control is implemented through consensus-based ADMMs. In [23,24], bi-level optimization methods for voltage control are proposed to coordinate DESSs. Although these distributed approaches share the advantages of mitigating voltage violations in distribution networks, they suffer from the following three shortages. Firstly, their reliance on peer-to-peer (P2P) communication increases vulnerability to cyber-physical threats and communication failures [25]. Secondly, the explicit modeling of DER constraints leads to prohibitive computational costs in large-scale systems. Lastly, self-interested agents may manipulate local cost functions, compromising global optimization objectives [26].

To overcome the above challenges, a novel hierarchical voltage controller is presented in this paper to ensure voltage regulation in networks with large-scale DESS deployment. The proposed control method consists of two layers. In the upper layer, the MPC-based voltage controller is utilized to generate the aggregated active power reference trajectories for critical buses. In the lower layer, a broadcast-based controller (BBC) dispatches parameterized power regulation signals, enabling autonomous active power tracking by DESS units. The core contributions of this study can be summarized as follows:

• A two-layer design decouples slow-timescale optimization (upper layer MPC-based control) from fast-timescale distributed execution (lower-layer broadcast-based control), significantly reducing the computational complexity.
• A broadcast-based control law ensures provable alignment between local DESS self-optimization and global voltage objectives, eliminating incentives for cost function manipulation.
• The lower-layer controller eliminates peer-to-peer communication dependencies, enhancing resilience against cyber threats and packet losses.
• The IEEE 34-bus and 123-bus test feeders are utilized to validate the efficacy of the proposed two-layer voltage control framework.

The rest of the paper is structured as follows. Section 2 outlines the distribution network model adopted in this study. The proposed two-layer voltage control scheme is detailed in Section 3. Section 4 conducts various case studies using the IEEE 34-bus and 123-bus test feeders. Section 5 provides the conclusion.

Notation: For any matrix $\mathit{F}\in {ℝ}^{n\times m}$, ${\mathit{F}}^{\top }$ is used to denote its transpose. Given a column vector $\mathit{x}\in {ℝ}^n$ and a symmetric matrix $\Pi \in {ℝ}^{n\times n}$ we define ${‖\mathit{x}‖}_{\Pi }^2={\mathit{x}}^{\top }\Pi \mathit{x}$. ${\mathit{I}}_n\in {ℝ}^{n\times n}$ represents an identity matrix.

2. System Description

This section presents the distribution network model adopted for implementing the proposed voltage control approach.

Without loss of generality, this study modelled an active distribution system consisting of N+1 buses, represented by the set $\mathcal{N}=\{0, 1,\dots , N\}$. The network topology is characterized by a branch set $\mathcal{I}:=\{(i,j)\}\subseteq \mathcal{N}\times \mathcal{N}$ with $|ℐ|=N$. Specifically, node 0 serves as the reference bus connected to the upstream grid, with its voltage magnitude fixed at the nominal value. For each bus i, V_i, p_i, and q_i denote the magnitude of its voltage magnitude and active and reactive power injection, respectively. The resistance and reactance parameters of branch (i, j) are defined as r_ij and x_ij. P_ij and Q_ij are the active and reactive power from bus i to bus j, respectively. Based on the DistFlow equations [27], the power flow to model the system can be written as:

$$P_{ij}-{\displaystyle \sum _{k\in {\mathcal{N}}_j}{P}_{jk}}=-p_j+r_{ij}{\displaystyle \frac{P_{ij}^2+Q_{ij}^2}{V_i^2}}$$

(1)

$$Q_{ij}-{\displaystyle \sum _{k\in {\mathcal{N}}_j}{Q}_{jk}}=-q_j+x_{ij}\frac{P_{ij}^2+Q_{ij}^2}{V_i^2}$$

(2)

$$V_i^2-V_j^2=2(r_{ij}{P}_{ij}+x_{ij}{Q}_{ij})-(r_{ij}^2+x_{ij}^2){\displaystyle \frac{P_{ij}^2+Q_{ij}^2}{V_i^2}}$$

(3)

Then, to simplify the calculation, it was assumed that: (a) thFe loss is negligible in comparison to the line power flow; (b) the voltage profile is relatively flat, i.e., $V_i^2-V_j^2\approx 2(V_i-V_j)$. The linearized DistFlow Equations (1)–(3) are linearized as follows [28]:

$$P_{ij}-{\displaystyle \sum _{k\in {\mathcal{N}}_j}{P}_{jk}}=-p_j$$

(4)

$$Q_{ij}-{\displaystyle \sum _{k\in {\mathcal{N}}_j}{Q}_{jk}}=-q_j$$

(5)

$$V_i-V_j=r_{ij}{P}_{ij}+x_{ij}{Q}_{ij}$$

(6)

To simplify expression, (4)–(6) are rewritten in the following compact form:

$$\mathit{V}=\mathit{Rp}+\mathit{Xq}+V_0{1}_N$$

(7)

where vectors $\mathit{V}={[V_1,V_2,\dots ,V_N]}^T\in {ℝ}^N$, $\mathit{p}={[p_1,p_2,\dots ,p_N]}^T\in {ℝ}^N$, and $\mathit{q}={[q_1,q_2,\dots ,q_N]}^T\in {ℝ}^N$ denote the bus voltages, active power injections, and reactive power injections, respectively $\mathit{R}\in {ℝ}^{N\times N}$ and $\mathit{X}\in {ℝ}^{N\times N}$ are the sensitivity matrices. $V_0$ is the voltage magnitude of bus 0. $1_N$ is a vector with all ones.

3. Proposed Control Strategy

In this section, to effectively coordinate massive DEESs, a two-layer voltage controller is presented to regulate voltage in distribution networks.

As illustrated in Figure 1, the proposed hierarchical control framework operates in two layers. In the upper layer controller, the MPC-based controller generates optimal power dispatch trajectories for critical buses, which are equipped with aggregated DEESs. In the lower layer controller, based on the control signals in the upper-layer controller, the broadcast-controller center broadcasts the Lagrangian multipliers. Then, each DEES updates its active power setpoints locally. Subsequently, the aforementioned procedures will be carried out in an iterative manner.

3.1. Upper Layer Controller

The upper-layer controller aims to mitigate voltage violations by coordinating aggregated DESS active power. By utilizing the linearized DistFlow model described in (7), the voltage control problem is structured as a quadratic programming (QP) to minimize operational costs while enforcing voltage constraints. The optimization objective and constraints are defined as follows:

$$\min \frac{1}{2}\left({‖{\mathit{p}}_g(k)‖}_{\mathit{\beta }}^2+{‖\mathit{\epsilon }(k)‖}_{\mathit{\chi }}^2+{‖\mathit{\delta }(k)‖}_{\mathit{\gamma }}^2\right)$$

(8)

$$\mathrm{s}.\mathrm{t}. {\mathit{V}}^{\min }-\mathit{\epsilon }\le \mathit{V}\le {\mathit{V}}^{\max }+\mathit{\delta }$$

(9)

$$\mathit{V}=\mathit{Rp}+\mathit{Xq}+V_0{1}_N$$

(10)

$$0\le {\mathit{p}}_d\le {\mathit{p}}_d^{\max }$$

(11)

$$0\le {\mathit{p}}_c\le {\mathit{p}}_c^{\max }$$

(12)

$${\mathit{p}}_g=-{\mathit{p}}_c+{\mathit{p}}_d$$

(13)

where ${\mathit{p}}_g(k)$ denote the active power of aggregated DESSs at instant k. $\mathit{\epsilon }(k)$ and $\mathit{\delta }(k)$ denote the slack variables, which convert the voltage constraint into the soft constraint. The matrices $\mathit{\beta }$, $\mathit{\chi }$, and $\mathbf{\gamma }$ denote diagonal matrices with positive weights. (10) represents the linearized DistFlow model. Constraints (11)–(13) define the lower and upper bounds of DESSs’ active power output. ${\mathit{p}}_d$ and ${\mathit{p}}_c$ denote the discharge and charge active power of DESSs. ${\mathit{p}}_c^{\max }$ and ${\mathit{p}}_d^{\max }$ denote the maximum of charge and discharge active power of aggregated DESSs.

Based on the above-defined elements, the optimization problem (8)–(13) represents a box-constrained QP, which can be conveniently addressed using the GUROBI solver [29]. By solving problem (8)–(13), the optimal set-points for the aggregated DESSs of each bus can be determined.

3.2. Lower-Layer Controller

Based on the results of (8)–(13), the active power setpoint of each DESSs in each bus (i.e., we take bus i as an example in the following) is determined through solving the following QP problem:

$$\min {\displaystyle \frac{1}{2}}{\displaystyle \sum _{j\in {\mathcal{N}}_i}{\beta }^{i,j}\left({\left(p_d^{i,j}(k)\right)}^2+{\left(p_c^{i,j}(k)\right)}^2\right)}$$

(14)

$$\mathrm{s}.\mathrm{t}.-p_{c,\max }^{i,j}\le -p_c^{i,j}\le 0\le p_d^{i,j}\le p_{d,\max }^{i,j}, \forall j\in {\mathcal{N}}_i$$

(15)

$$E^{i,j}(k)=E^{i,j}(k-1)+\left({\gamma }^{i,j}{p}_c^{i,j}-{\displaystyle \frac{p_d^{i,j}}{{\gamma }^{i,j}}}\right)\Delta t, \forall j\in {\mathcal{N}}_i$$

(16)

$${\eta }_{\min }^{i,j}{E}_{\max }^{i,j}\le E^{i,j}(k)\le {\eta }_{\max }^{i,j}{E}_{\max }^{i,j}, \forall j\in {\mathcal{N}}_i$$

(17)

$$E^{i,j}(0)=E_0^{i,j}, \forall j\in {\mathcal{N}}_i$$

(18)

$${\displaystyle \sum _{j\in {\mathcal{N}}_i}(p_d^{i,j}-p_c^{i,j})}=p_s^i$$

(19)

where $N_i$ denotes the index set of DESSs in bus i ($i\in \mathcal{N}$). ${\beta }^{i,j}$ denotes the coefficient of the cost function of DESS j ($j\in {\mathcal{N}}_i$). $p_d^{i,j}$ and $p_c^{i,j}$ denote the discharge and charge active power of DESS j, respectively. (15)–(18) denote the operation constraints of DESSs in bus i. $p_{d,\max }^{i,j}$ and $p_{c,\max }^{i,j}$ denote the maximum value of $p_d^{i,j}$ and $p_c^{i,j}$, respectively. $E^{i,j}$ denotes the state of charge of DESS j. ${\gamma }^{i,j}$ represents the operational efficiency of DESS j. $\Delta t$ is the sample interval. ${\eta }_{\min }^{i,j}$ and ${\eta }_{\max }^{i,j}$ denote the maximum and minimum normalized unit limits of charge, respectively. $E_{\max }^{i,j}$ represents the maximum capacity of DESS j; $E_0^{i,j}$ denotes the initial state of charge of DESS j. (19) denotes the aggregated active power demand, where $p_s^i$ denotes the active power demand of bus i ($i\in \mathcal{N}$) obtained in (8)–(13).

However, as mentioned above, the QP problem (14)–(19) has the following shortcomings:

(1)

The computation complexity can be dramatic with the growing connection with DESSs;

(2)

The missing data caused by communication interruption may lead to a significant degradation in the control performance of (14)–(19).

To address these challenges, a BBC is proposed to dynamically track the aggregated active power reference from the upper layer, even under partial communication losses. This controller employs Lagrangian multiplier updates to align local DESS operations with global objectives, ensuring robustness against data interruptions.

Firstly, to simplify the expression, the optimization problem (14)–(19) is rewritten as follows:

$$\min {\displaystyle \frac{1}{2}}{\displaystyle \sum _{j\in {\mathcal{N}}_i}{\beta }^{i,j}{‖{\mathit{p}}_g^{i,j}‖}_2^2}$$

(20)

$$\mathrm{s}.\mathrm{t}. {\mathit{A}}^{i,j}{\mathit{p}}_g^{i,j}\le {\mathit{b}}^{i,j},\forall j\in {\mathcal{N}}_i$$

(21)

$${\displaystyle \sum _{j\in {\mathcal{N}}_i}{1}_2^{\top }{\mathit{p}}_g^{i,j}}=p_s^i$$

(22)

where ${\mathit{p}}_g^{i,j}={[p_d^{i,j},p_c^{i,j}]}^{\top }$ denotes the vector of discharge and charge power of DESSs j ($j\in {\mathcal{N}}_i$); ${\mathit{A}}^{i,j}$ and ${\mathit{b}}^{i,j}$ denote the operation constraint of DESSs j in (15)–(18), which are arranged as:

$${\mathit{A}}^{i,j}=\left[\begin{array}{cc}1& 0\\ 0& 1\\ {\displaystyle \frac{-\Delta t}{{\gamma }^{i,j}}}& {\gamma }^{i,j}\Delta t\\ {\displaystyle \frac{\Delta t}{{\gamma }^{i,j}}}& -{\gamma }^{i,j}\Delta t\end{array}\right],{\mathit{b}}^{i,j}=\left[\begin{array}{c}{p}_{d,\max }^{i,j}\\ p_{c,\max }^{i,j}\\ {\eta }_{\max }^{i,j}{E}_{\max }^{i,j}-E^{i,j}(k-1)\\ E^{i,j}(k-1)-{\eta }_{\min }^{i,j}{E}_{\max }^{i,j}\end{array}\right]$$

(23)

We now consider the Lagrangian function related to the optimization problem (20)–(22), which is expressed as:

$$\underset{\lambda \ge 0}{\max }\underset{{\mathit{p}}_g^{i,j}\in {\mathcal{P}}^{i,j}}{\min }{\displaystyle \frac{1}{2}}{\displaystyle \sum _{j\in {\mathcal{N}}_i}{\beta }^{i,j}{‖{\mathit{p}}_g^{i,j}‖}_2^2}+\lambda \left({\displaystyle \sum _{j\in {\mathcal{N}}_i}{1}_2^{\top }{\mathit{p}}_g^{i,j}}-p_s^i\right)$$

(24)

where ${\mathcal{P}}^{i,j}$ denotes the operation constraints (21). $\lambda$ is the Lagrange multiplier corresponding to constraint (22), which is used to ensure the consistency of the local DESS optimization with the global voltage objective.

Since problem (24) is strictly convex and separable, (24) can solved iteratively via the gather-and-broadcast dual decomposition method. Specifically, at the ${\tau }^{th}$ iteration ($\tau \ge 2$), the broadcast-based method consists of the following steps, which are also illustrated in Figure 2.

(1)

The BBC collects the difference between the aggregated active power and the demand (i.e., ${\displaystyle \sum _{j\in {\mathcal{N}}_i}{1}_2^{\top }{\mathit{p}}_g^{i,j}}-p_s^i$) for the real-time updating of the Lagrangian multiplier $\mathsf{\lambda }$:

$$\lambda (\tau )=\lambda (\tau -1)-\rho \left({\displaystyle \sum _{j\in {\mathcal{N}}_i}{1}_2^{\top }{\mathit{p}}_g^{i,j}(\tau -1)}-p_s^i\right)$$

(25)

where $\rho$ is a small positive constant.

(2)

The updated Lagrangian multiplier $\lambda (\tau )$ is sent to each DESSs.

(3)

After receiving the updated Lagrangian multiplier $\lambda (\tau )$ in (8), the active power point of each DESS j ($j\in {\mathcal{N}}_i$) is updated by:

$$\min {\displaystyle \frac{1}{2}}{\beta }^{i,j}{‖{\mathit{p}}_g^{i,j}‖}_2^2-\lambda {(\tau )}^{\top }{1}_2^{\top }{\mathit{p}}_g^{i,j}$$

(26)

$$\mathrm{s}.\mathrm{t}. {\mathit{A}}^{i,j}{\mathit{p}}_g^{i,j}\le {\mathit{b}}^{i,j}$$

(27)

Note that, if DESS j has not received the newly updated Lagrangian multiplier $\lambda (\tau )$, the active power point of each DESS j remains the same as in the ${(\tau -1)}^{th}$ iteration. This updated rule can improve the robustness of the proposed control approach to the communication interrupt (see the case study for illustration).

3.3. Implementing of the Proposed Approach

To better illustrate the proposed methods, the implementation of the proposed two-layer voltage control approach is illustrated in Figure 3. In the proposed two-layer voltage control approach, there is an upper layer controller operated with a slow time period $t_s$ of 5 min and a lower layer controller operated at a fast timescale $t_f$ of 15 s. The implementation of proposed two-layer voltage controller is summarized as follows:

(1)

Data Collection: Obtain the real-time measurement of voltage magnitudes and active power injections.

(2)

MPC Optimization: At the beginning of each $t_s$, solve the optimization problem (8)–(13) to obtain the aggregated active power reference trajectories for critical buses.

(3)

Broadcast Execution: For the rest time of each $t_s$, each bus employs the BBC to achieve autonomous active power tracking by DESS units.

(4)

Simulation Cycle: Repeat steps (1)–(3) until the end of the simulation.

Figure 3. Schematic of the hierarchical voltage control structure with upper-layer MPC and lower-layer broadcast control loop.

Figure 3. Schematic of the hierarchical voltage control structure with upper-layer MPC and lower-layer broadcast control loop.

4. Case Study

4.1. IEEE 34-Bus Test Feeder

The modified IEEE 34-bus test feeder configuration is shown in Figure 4. The initial line impedance and shunt admittance parameters were obtained from [30]. The system operated with base values of 4.16 kV (voltage) and 1 MVA (power). It incorporated 11 photovoltaic units and 6 DESSs installed at buses {13, 18, 23, 28, 31, 33}. To investigate the impact of PV intermittency on voltage stability, the line R/X ratio was adjusted within [1,2]. Each DESS-equipped bus hosted 20 identical energy storage units, whose parameters are tabulated in

Table 1. DESS unit parameters.

Parameters	Value
$p_{d,\max }^{i,j}$	−8 kW
$p_{c,\max }^{i,j}$	8 kW
$E_{\max }^{i,j}$	25 kW·h
$E_0^{i,j}$	15 kW·h
${\eta }_{\max }^{i,j}$	80%
${\eta }_{\min }^{i,j}$	20%
${\gamma }^{i,j}$	96%

. For computational tractability, uniform DESS characteristics were assumed. The substation bus (Bus 0) voltage was fixed at 1.0 per unit (p.u.), and the voltage regulation boundary was defined as [0.95, 1.05] p.u. Figure 5 shows the daily profiles of PV generation and active load. The PV power solely represents its predicted values for all the PVs, and the real values of all PVs’ power are normally distributed with the predicted value as the mean. This simulation was executed on a 64-bit Windows 10 PC featuring a 2.50 GHz Intel Core i5-13490F dual-core CPU and 32.0 GB RAM, using MATLAB platform with GUROBI Optimizer [29].

Figure 6 depicts the voltage magnitudes at each bus within the test system under uncontrolled conditions. Evident voltage violations exceeding the [0.95, 1.05] p.u. boundary occur during peak PV generation periods. Subsequently, the proposed two-layer voltage control framework was implemented to coordinate DESS operations. Figure 7 demonstrates the resulting voltage profiles, where the majority of buses are regulated within acceptable limits. Minor transient deviations observed in several instances are attributed to inaccuracies in the linearized power flow model. Figure 8 presents the aggregated active power dispatch of DESSs across the six equipped buses, while Figure 9 details the individual DESS operation setpoints at bus 33, which is particularly vulnerable to voltage violations due to the cumulative impact of line impedance [4]. From Figure 8 and Figure 9, it is clear that the proposed approach can achieve decentralized power tracking.

To assess the practical implementation viability of the proposed control framework, the computation efficiency of both hierarchical layers was evaluated. Average computation times for the upper layer MPC and lower layer broadcast control were 5.5 ms and 66.7 ms (i.e., much lower than the control cycle of 15 s), respectively, demonstrating the feasibility of the real-time application of the proposed approach.

Building on the decentralized Lagrangian updating mechanism, the BBC significantly reduces communication burden overhead compared to the traditional P2P architectures. In the BBC, only a scalar parameter (i.e., the Lagrangian multiplier λ) needs to be broadcast to all DESSs in each control cycle (15 s). Assuming λ is transmitted as a 32-bit single-precision floating-point number, the data volume per broadcast is 4 bytes. For a bus with $N_D$ DESSs, traditional P2P communication requires each bus to exchange control signals with $N_D$ DESSs, resulting in $N_D\times (N_D-1)$ interactions per cycle. Taking $N_D=20$ as an example, the conventional method requires 380 communications per cycle, while the proposed approach requires only 1 communication, reducing the communication burden from $O(N^2)$ to $O(1)$. In summary, under a 15 s control cycle, the broadcast method consumes approximately 0.27 bytes/s, whereas P2P communication would demand 101.3 bytes/s. By minimizing the communication frequency and data volume, the proposed method can dramatically reduce the communication load, demonstrating superior scalability for large-scale distributed systems.

To validate the robustness of the proposed method, we evaluated its control performance under communication outages of varying severity. Figure 10 demonstrates the aggregated active power tracking accuracy of DESSs across 0–60% data loss scenarios, highlighting the proposed controller’s resilience against communication disruptions. Figure 11 illustrates the voltage profiles at bus 33 under different communication loss rates, demonstrating that the proposed strategy maintains bus voltages within the 0.95 to 1.05 p.u. range even with 60% communication loss, except for brief voltage excursions during peak PV generation periods.

To evaluate the proposed method’s robustness to communication latency, the voltage regulation performance was assessed under a 15-s communication delay condition. As shown in Figure 12, the voltage profile of bus 33 can still be regulated within the acceptable range even with a 15-s communication delay, demonstrating the robustness of the proposed method against large communication delays.

To validate the accuracy of the linearized model used in the control design, Figure 13 shows the approximation error of the linearized DistFlow model (7). The observed error remains consistently low, i.e., approximately 0.3% with respective to the nominal voltage magnitude, demonstrating the accuracy of the linearized model (7).

To validate the advantages of the proposed method, we compared the control performance of the two-timescale voltage control approach in [31], distributed voltage control approach in [4] and the proposed approach with communication loss (i.e., scenarios involving data loss). The voltage control performance is qualified by defining the average voltage violation (AVV) as follows:

$$AVV={\displaystyle \frac{1}{N_v}}{\displaystyle \sum _{k\in {\mathcal{N}}_v}\left(\left|\max \left(V(k)-V^{\max },0\right)\right|+\left|\min \left(V(k)-V^{\min },0\right)\right|\right)}$$

(28)

where N_v denotes the set of samples when voltage violations occur, while N_v denotes the number of moments in set N_v.

Figure 14 shows the voltage profile of bus 33 with the methods in [4,31] and the proposed method under 60% communication loss scenario.

Table 2. AVV and maximum and minimum voltages under various cases.

AVV	Maximum Voltage Magnitude (p.u.)	Minimum Voltage Magnitude (p.u.)	Cases
$5.8\times {10}^{-4}$	1.0509	0.9488	With the proposed method
$2.3\times {10}^{-3}$	1.0560	0.9456	With the method in [4]
$1.2\times {10}^{-3}$	1.0533	0.9470	With the method in [31]
$8.6\times {10}^{-3}$	1.0651	0.9321	Without control

shows the quantitative results of voltage control effects (e.g., AVV and maximum and minimum voltage magnitudes) for bus 33 (i.e., the most sensitive bus) under various cases. From Figure 14 and Table 2, it is clear that the proposed method can reduce the 93.7% AVV compared with the case without control, and achieves a better voltage control performance than the methods in [4,31].

4.2. IEEE 123-Bus Test Feeder

To further validate the effectiveness of the proposed controller in large systems, the IEEE 123-bus feeder was emplyed for testing purposes. Figure 15 shows the diagram of the modified IEEE 123-bus test feeder.

Table 3. Installed bus numbers of PVs and DESSs in the modified IEEE 123-bus test feeder.

Device Type	Installed Bus Numbers
PVs	1, 20, 28, 32, 34, 39, 45, 50, 55, 57, 61, 69, 74, 81, 86, 92, 100, 107, 114, 117, 120, 122
DESSs	20, 28, 31,39, 45, 52, 55, 57, 61, 69, 74, 77, 92, 107, 117, 122

shows the installed bus numbers of PVs and DESSs.

Figure 16 and Figure 17 show the voltage profile without and with the proposed approach, respectively. From Figure 16 and Figure 17, it is clear that the voltage violations are mitigated effectively by the proposed approach, which demonstrates the effectiveness and scalability of the proposed scheme.

5. Conclusions

This paper introduces a hierarchical voltage control framework leveraging DESSs to address voltage violations in distribution networks. The proposed hierarchical architecture integrates MPC in the upper layer to compute aggregated active power reference trajectories for critical buses, while a BBC in the lower layer ensures autonomous DESS power tracking through Lagrangian multiplier updates. This design mitigates the scalability limitations of centralized approaches and cyber vulnerabilities of peer-to-peer distributed methods. Simulation studies on the modified IEEE 34-bus and 123-bus feeders validate its effectiveness, demonstrating voltage regulation within ±5% limits under high photovoltaic penetration and maintaining robustness even with 60% communication outages. Future research will focus on model-free control methods, extensions to unbalanced three-phase systems, communication-constrained robustness enhancements, and coordinated optimization with other distributed energy resources.