In this study, I present a systematic layout design method for a thermal power plant integrated with a hybrid energy storage system dedicated to frequency regulation. The proposed approach formulates the arrangement of prefabricated energy storage units, including lithium-ion battery systems and flywheel systems, as a mixed-integer linear programming problem. I combine exact optimization with a metaheuristic-driven iterative reduction strategy to handle large-scale instances within practical engineering time limits. The model incorporates safety distance constraints, cable routing costs, operational maintenance convenience, and layout aesthetics through dynamically weighted objective functions. I validate the method using two realistic engineering scenarios with different storage configurations. The results demonstrate that the approach can efficiently generate feasible and high-quality layout schemes, providing valuable decision support for actual power plant retrofit projects.
1. Introduction
With the rapid deployment of renewable energy sources such as wind and solar power, the grid frequency regulation burden on conventional thermal power units has become increasingly severe. According to recent energy statistics, renewable energy accounts for more than half of the total installed capacity in many countries. The stochastic and intermittent nature of renewable generation causes frequent and large frequency deviations, which require fast and accurate regulation resources. Traditional thermal units, constrained by their inherent mechanical and thermodynamic characteristics, often exhibit slow response times and low regulation precision when tracking automatic generation control signals. This leads to over-regulation, delayed regulation, and increased wear on equipment, ultimately undermining both operational safety and economic performance.
Electrochemical energy storage systems, particularly lithium-ion based energy storage batteries, have been widely adopted to assist thermal units in frequency regulation. These systems offer high energy capacity, accurate response, and flexible control. However, they are less effective when dealing with high-frequency, high-amplitude power fluctuations due to their limited ramp rates and cycle life. To overcome this limitation, hybrid energy storage systems combining lithium-ion batteries with flywheel energy storage have been proposed. Flywheels provide extremely fast response, high instantaneous power, and virtually unlimited cycle life, making them ideal for high-frequency components of regulation signals. The complementary characteristics of energy storage batteries and flywheels form a powerful hybrid system that can significantly improve the overall frequency regulation performance of thermal power plants.
While the technical benefits of hybrid storage are well recognized, the physical layout design of such systems within a limited power plant area remains a challenging practical problem. Unlike greenfield installations, thermal power plants usually have constrained spaces, existing infrastructures, roads, and safety requirements. The layout must consider not only geometric non-overlap constraints but also safety clearances between different types of prefabricated cabinets, cable connection costs, maintenance accessibility, and even visual aesthetics. These requirements make the layout problem a complex combinatorial optimization task, which falls under the category of facility layout problems.
Facility layout problems are known to be NP-hard, and exact methods often fail to find optimal solutions in reasonable time when the number of facilities increases. On the other hand, pure metaheuristic approaches may suffer from poor interpretability and parameter sensitivity. In this context, I propose a hybrid optimization method that integrates a mixed-integer linear programming formulation with a metaheuristic search framework. The exact solver is used as the core engine, while the metaheuristic strategy periodically reduces problem complexity by fixing a subset of facility positions and orientations, allowing the solver to focus on the remaining variables. A dynamic weighting mechanism adjusts the relative importance of multiple objectives during the optimization process. I evaluate the proposed method on two actual engineering scenarios, one with only lithium battery energy storage and one with a combined battery-flywheel hybrid system. The results show that the method produces practical layout designs that satisfy safety codes and minimize total costs.
2. Mathematical Formulation
In this section, I present the mathematical model for the hybrid energy storage layout design problem. The model is based on several simplifying assumptions that still retain the essential characteristics of the real-world problem.
2.1 Site and Facility Modeling
The available area is modeled as a rectangle of known length and width. A Cartesian coordinate system is defined with its origin at one corner of the rectangle, with the horizontal axis denoted as the \(X\)-axis and the vertical axis as the \(Y\)-axis. Each prefabricated energy storage unit is approximated by its axis-aligned bounding box, which is also a rectangle of known dimensions. The orientation of each facility can be either the natural orientation (long side parallel to \(X\)-axis) or the rotated orientation (long side parallel to \(Y\)-axis). The position of a facility is represented by the coordinates of its lower-left corner. The geometric center of the rectangle serves as the connection point for cable routing between facilities.
In addition, any fixed obstacles inside the site, such as existing roads, drainage channels, or immovable equipment, are also modeled as axis-aligned rectangles. These obstacles act as forbidden zones that cannot be occupied by any facility. Figure (to be inserted) illustrates the site model used in this study.
Let \(B_x\) and \(B_y\) denote the length and width of the site, respectively. For each facility \(i\), let \(L_i^{\text{len}}\) and \(L_i^{\text{wid}}\) be the actual length and width of the prefabricated cabinet. The orientation is represented by a binary variable \(O_i^{\text{orient}}\) where 0 indicates the natural orientation and 1 indicates the rotated orientation. Then the effective length and width of facility \(i\) in the current orientation are given by:
\[
L_i^{\text{eff}} = O_i^{\text{orient}} L_i^{\text{wid}} + (1 – O_i^{\text{orient}}) L_i^{\text{len}}
\]
\[
W_i^{\text{eff}} = O_i^{\text{orient}} L_i^{\text{len}} + (1 – O_i^{\text{orient}}) L_i^{\text{wid}}
\]
Let \((x_i, y_i)\) be the coordinates of the lower-left corner of facility \(i\). The geometric center \((cx_i, cy_i)\) of the facility is then:
\[
cx_i = x_i + \frac{L_i^{\text{eff}}}{2}
\]
\[
cy_i = y_i + \frac{W_i^{\text{eff}}}{2}
\]
The above formulation allows me to handle the two possible orientations without explicitly enumerating them, which is crucial for maintaining the linearity of the model.
2.2 Constraints
The layout must satisfy several categories of constraints: boundary constraints, obstacle avoidance constraints, safety distance constraints, and separation constraints between facilities.
First, every facility must lie completely within the site boundaries while maintaining a minimum clearance distance \(D_B\) to the boundary. This is expressed as:
\[
x_i \geq D_B
\]
\[
y_i \geq D_B
\]
\[
x_i + L_i^{\text{eff}} + D_B \leq B_x
\]
\[
y_i + W_i^{\text{eff}} + D_B \leq B_y
\]
If there are fixed obstacles, similar clearance constraints are imposed between a facility and each obstacle. For obstacle \(k\) with lower-left corner \((x_k^{\text{obs}}, y_k^{\text{obs}})\), length \(L_k^{\text{obs}}\), and width \(W_k^{\text{obs}}\), the non-overlap conditions can be linearized using the standard big-M method. However, in the cases studied here, the only obstacles are road crossings, which are handled as forbidden rectangular regions with a required minimum distance to any facility.
Second, any two facilities must not overlap. The separation constraints are expressed using a set of binary variables that determine the relative position of one facility with respect to another. For facilities \(A\) and \(B\), define four binary variables: \(n_{AB}\) (B is north of A), \(s_{AB}\) (B is south of A), \(w_{AB}\) (B is west of A), and \(e_{AB}\) (B is east of A). At least one of these must be true, and opposite directions cannot be simultaneously true. Thus:
\[
1 \leq n_{AB} + s_{AB} + w_{AB} + e_{AB} \leq 2
\]
\[
n_{AB} + s_{AB} = 1
\]
\[
w_{AB} + e_{AB} = 1
\]
Additionally, I introduce four more binary variables \(u_{AB}, d_{AB}, r_{AB}, l_{AB}\) to indicate the direction in which the safety distance constraint is actually enforced. Only one direction is active at a time:
\[
u_{AB} + d_{AB} + r_{AB} + l_{AB} \leq 1
\]
These variables are linked to the relative position variables as follows:
\[
n_{AB} \geq u_{AB}
\]
\[
s_{AB} \geq d_{AB}
\]
\[
w_{AB} \geq l_{AB}
\]
\[
e_{AB} \geq r_{AB}
\]
Then the safety distance \(D_{AB}\) between facilities \(A\) and \(B\) is enforced by the following constraints, where \(M\) is a sufficiently large constant (chosen as 5 to 10 times the site length):
\[
D_{AB} + (r_{AB} – 1)M \leq x_B – (x_A + L_A^{\text{eff}})
\]
\[
D_{AB} + (l_{AB} – 1)M \leq x_A – (x_B + L_B^{\text{eff}})
\]
\[
D_{AB} + (u_{AB} – 1)M \leq y_B – (y_A + W_A^{\text{eff}})
\]
\[
D_{AB} + (d_{AB} – 1)M \leq y_A – (y_B + W_B^{\text{eff}})
\]
These constraints ensure that if, for example, facility B is placed to the east of A (\(r_{AB}=1\)), then the horizontal coordinate difference must be at least \(D_{AB}\). In all other directions, the corresponding inequality becomes automatically satisfied due to the large negative penalty introduced by \((1 – M)\).
2.3 Objective Functions
The layout design problem involves three main objectives that reflect the economic and operational considerations. I describe each objective in detail below.
2.3.1 Cable Construction Cost
The first objective minimizes the total cost of cables and cable trenches between facilities that are electrically connected. The set of electrical connections \(E\) is defined based on the system architecture. For a hybrid storage system, the typical connections include:
\[
E = \{ \{\text{EHV cabinet}, \text{station transformer cabinet}\}, \{\text{EHV cabinet}, \text{LV cabinet}\}, \{\text{EHV cabinet}, \text{PCS cabinet}\}, \{\text{PCS cabinet}, \text{battery cabinet}\}, \{\text{EHV cabinet}, \text{flywheel PCS cabinet}\}, \{\text{flywheel PCS cabinet}, \text{flywheel cabinet}\} \}
\]
Let \(L(i,j)\) be the Manhattan distance between the geometric centers of two connected facilities. The cable cost is:
\[
C_1 = \sum_{(i,j) \in E} L(i,j) \cdot f_1(i,j)
\]
where \(f_1(i,j)\) is the cost per unit length of cable, including the cable price and the cost of digging the cable trench. Since the cable types and quantities differ for various connections, \(f_1\) varies with the connection pair.
2.3.2 Operation and Maintenance Cost
The second objective captures the convenience of operation and maintenance. Certain related facilities should be placed close together to reduce personnel walking distances and simplify management. This is modeled through non-logistical relationship factors, following standard facility layout methodology.
For battery systems, each battery cabinet is connected to one power conversion system (PCS) cabinet. The maintenance cost is proportional to the distance between them. Additionally, all battery cabinets of the same type should be clustered together to facilitate routine inspections. The corresponding terms are:
\[
l_{\text{bat,pcs}} = \frac{1}{2} \sum_{i=1}^{n_{\text{bat}}} \sum_{j=1}^{n_{\text{pcs}}} | cx_{i}^{\text{bat}} – cx_{j}^{\text{pcs}} | + | cy_{i}^{\text{bat}} – cy_{j}^{\text{pcs}} |, \quad (i,j) \in E
\]
\[
l_{\text{bat,bat}} = \sum_{i=1}^{n_{\text{bat}}} \left( | cx_{i}^{\text{bat}} – cx_{\text{center}}^{\text{bat}} | + | cy_{i}^{\text{bat}} – cy_{\text{center}}^{\text{bat}} | \right)
\]
where \(n_{\text{bat}}\) is the number of battery cabinets, \(n_{\text{pcs}}\) is the number of battery-side PCS cabinets, and \((cx_{\text{center}}^{\text{bat}}, cy_{\text{center}}^{\text{bat}})\) is the centroid of all battery cabinets.
For flywheel systems, a typical configuration is “one-to-many”, e.g., one flywheel PCS cabinet connected to four flywheel cabinets (a “one-to-four” group). Flywheels have high rotational kinetic energy and require strict safety isolation. Therefore, all flywheel cabinets belonging to the same group should be placed in a compact cluster, and no other facilities should intrude into the gap between them. The non-logistical scale for flywheel groups is:
\[
l_{\text{fw,pcs}} = \frac{1}{2} \sum_{k} \sum_{j=1}^{n_{\text{fpcs}}} \left( | cx_{\text{center},k}^{\text{fw}} – cx_{j}^{\text{fpcs}} | + | cy_{\text{center},k}^{\text{fw}} – cy_{j}^{\text{fpcs}} | \right)
\]
where \(k\) indexes the flywheel groups, \(n_{\text{fpcs}}\) is the number of flywheel PCS cabinets in group \(k\), and \((cx_{\text{center},k}^{\text{fw}}, cy_{\text{center},k}^{\text{fw}})\) is the centroid of all flywheel cabinets in that group. In addition, to keep flywheels away from other equipment, a penalty is added based on the distance between each flywheel cabinet and the geometric center of all non-flywheel facilities:
\[
l_{\text{fw,others}} = \sum_{i=1}^{n_{\text{fw}}} \left( | cx_{i}^{\text{fw}} – cx_{\text{others}} | + | cy_{i}^{\text{fw}} – cy_{\text{others}} | \right)
\]
where \(n_{\text{fw}}\) is the total number of flywheel cabinets and \((cx_{\text{others}}, cy_{\text{others}})\) is the centroid of all other facilities. This penalty encourages flywheels to be placed away from the main operational areas, improving overall safety.
I combine these terms using non-logistical relationship factors \(f_2\):
\[
C_2 = f_{\text{bat,pcs}} \cdot l_{\text{bat,pcs}} + f_{\text{bat,bat}} \cdot l_{\text{bat,bat}} + f_{\text{fw,pcs}} \cdot l_{\text{fw,pcs}} + f_{\text{fw,others}} \cdot l_{\text{fw,others}}
\]
The factors \(f_2\) are chosen empirically based on the relative importance of each relationship. In my implementation, I set these factors proportional to the number of personnel involved in related maintenance procedures.
2.3.3 Layout Aesthetics
Aesthetically pleasing layouts not only improve the image of the power plant but also reduce the chance of misoperation caused by irregular cable routing. I introduce an alignment objective that penalizes cases where connected facilities are not aligned along the \(X\)-axis or the \(Y\)-axis. For each connected pair \((i,j) \in E\), I define two binary variables \(t_{ij}^x\) and \(t_{ij}^y\), which indicate whether there is misalignment in the respective axis. The objective term is:
\[
C_3 = \sum_{(i,j) \in E} f_{\text{align}} \cdot (t_{ij}^x + t_{ij}^y)
\]
where \(f_{\text{align}}\) is a large positive penalty factor, and the variables satisfy:
\[
t_{ij}^x + t_{ij}^y \geq 1
\]
\[
t_{ij}^x, t_{ij}^y \in \{0,1\}
\]
If two facilities are aligned either horizontally or vertically, one of the two variables can be 0, and the penalty is significantly reduced. To exactly enforce alignment, I would need additional constraints involving the coordinates, but in the mixed-integer linear programming formulation, the above condition correctly penalizes cases where neither horizontal nor vertical alignment is satisfied.
2.3.4 Dynamic Weighting
The three objectives are combined into a single scalar objective with dynamic weights. The normalized objective is:
\[
F(s) = \alpha(s) \frac{C_1}{L_0} + \beta(s) \frac{C_2}{L_0} + \gamma(s) C_3
\]
where \(s\) is the iteration index, \(L_0\) is a scaling factor (e.g., the perimeter of the site) used to normalize the distances, and the weights \(\alpha, \beta, \gamma\) evolve linearly from initial values \((\alpha_0, \beta_0, \gamma_0)\) to final values \((\alpha_{\text{fin}}, \beta_{\text{fin}}, \gamma_{\text{fin}})\) over the total number of iterations \(S\):
\[
\alpha(s) = \alpha_0 + (\alpha_{\text{fin}} – \alpha_0) \frac{s}{S}
\]
\[
\beta(s) = \beta_0 + (\beta_{\text{fin}} – \beta_0) \frac{s}{S}
\]
\[
\gamma(s) = \gamma_0 + (\gamma_{\text{fin}} – \gamma_0) \frac{s}{S}
\]
with the constraint that the sum of the three weights equals 1 at every iteration. The dynamic weighting allows the optimizer to focus on cost-related objectives in the early stages and gradually increase the importance of operational convenience and aesthetics in later stages. This mimics the decision-making process of experienced design engineers who first locate the main electrical equipment and then fine-tune the layout for maintainability and appearance.
3. Optimization Strategy
Solving the mixed-integer linear programming model directly for a large number of facilities is computationally expensive. In practical engineering projects, the number of prefabricated cabinets can exceed 20, and the exact solver may not find a feasible solution within hours. To overcome this difficulty, I propose an iterative model reduction strategy that alternates between global optimization and local refinement.
The overall algorithm is structured as follows:
Step 1: Set a time limit \(T_{\text{init}}\) and solve the original mixed-integer linear programming problem. If an optimal solution is found, terminate. Otherwise, collect the best \(M_0\) solutions found within the time limit and form an initial population \(S_0\). These solutions represent diverse trade-offs among the objectives due to the dynamic weight adjustments.
Step 2: For each individual in the population, randomly select one facility and fix its position and orientation. Solve the reduced mixed-integer linear programming problem with the selected facility fixed, using the same time limit \(T_{\text{solve}}\). Collect the \(M_1\) best solutions from this step.
Step 3: Apply a mutation operation to a subset of the collected solutions. The mutation randomly flips the orientation of the already-fixed facility with a probability \(p_{\text{mut}}\). This operation introduces diversity and avoids premature convergence. The mutated solutions are added to the population to form set \(S_1\).
Step 4: Select a second facility to fix, preferably one that is electrically connected to or of the same type as the first fixed facility. This choice aims to reduce the coupling between variables and make the remaining subproblem easier to solve. Repeat the solving and collection steps to obtain the next population.
Step 5: If the relative improvement in the objective function is below a threshold \(\epsilon\) for two consecutive fixed iterations, the algorithm detects potential local convergence. In that case, one randomly selected fixed facility is unfixed, and the optimization continues with one fewer fixed variable. This “unlocking” mechanism allows the search to escape from local optima.
Step 6: The process terminates when all facilities have been fixed or when the global time limit is reached. The best solution among all populations is returned as the final layout.
To illustrate the computational gain of this strategy, consider a problem with \(n\) facilities. The original mixed-integer linear programming model has \(O(n^2)\) binary variables due to the relative position constraints. If \(k\) facilities are fixed, the number of free facilities is \(n-k\), and the number of binary variables decreases to \(O((n-k)^2)\). This quadratic reduction significantly improves the solver’s performance, as demonstrated in the case studies below.
The algorithm parameters are summarized in the following table:
| Parameter | Description | Typical Value |
|---|---|---|
| \(T_{\text{init}}\) | Initial solve time limit | 1–3 minutes |
| \(M_0\) | Initial population size | Number of facilities |
| \(M_1\) | Number of solutions collected after each solve | 10–25 |
| \(p_{\text{mut}}\) | Mutation probability | 0.2 |
| \(\epsilon\) | Convergence threshold | 0.05 (5%) |
4. Case Studies and Validation
I now apply the proposed method to two real engineering scenarios. The first scenario is a pure lithium battery frequency regulation system in a compact area. The second scenario is a hybrid battery-flywheel system in a larger area with a road crossing. Both cases are modeled and solved using the COPT optimization solver with the Python API. The algorithm is implemented using a custom iterative framework.
4.1 Case 1: Full Lithium Battery Energy Storage
The available site is a rectangle of length 40.3 m and width 33.5 m. A road of width 3.5 m runs through the site horizontally at the vertical center. This road is treated as a forbidden obstacle. The system includes 7 battery cabinets, 7 PCS cabinets, one high-voltage (EHV) cabinet, one low-voltage (LV) cabinet, and one station transformer cabinet. The dimensions and quantities are listed in the following table.
| Facility Type | Quantity | Dimensions (mm × mm) |
|---|---|---|
| EHV cabinet | 1 | 13000 × 3300 |
| LV cabinet | 1 | 12192 × 2800 |
| Station transformer cabinet | 1 | 5850 × 2800 |
| Battery PCS cabinet | 7 | 6058 × 2438 |
| Energy storage battery cabinet | 7 | 12192 × 2438 |
The total number of facilities is 17. I set the initial solve time limit \(T_{\text{init}} = 1\) minute. The initial weights are \(\alpha_0 = 0.7\), \(\beta_0 = 0.2\), \(\gamma_0 = 0.1\). The final weights are \(\alpha_{\text{fin}} = 0.5\), \(\beta_{\text{fin}} = 0.2\), \(\gamma_{\text{fin}} = 0.3\). The initial population size \(M_0\) is set to 17. During the iterative procedure, \(M_1 = 10\) and \(p_{\text{mut}} = 0.2\).
After the initial pre-solve, a representative solution from the initial population is shown in a visual representation. It can be observed that due to the limited available area, the general zones of each type of facility are roughly determined, but some positions still have room for improvement. The algorithm then fixes one facility at a time and re-solves the remaining subproblem. For example, after fixing one of the battery cabinets, the resulting layout shows a more organized arrangement of the other cabinets.
After multiple iterations and occasional unlocking steps, the final solution is obtained. The final layout places the EHV cabinet near the lower-left corner, with the battery cabinets and PCS cabinets arranged in two parallel rows below the central road. The station transformer and LV cabinets are placed on the left side. Compared to an actual manually designed layout, my algorithm achieves a very similar arrangement. The main difference is that the actual layout places the station transformer cabinet near the left boundary because of an external connection to a pole-mounted switch, which is not considered in the simplified model. This indicates that the algorithm is capable of reproducing the key design logic and can be adapted to additional external constraints when needed.
4.2 Case 2: Hybrid Battery-Flywheel Storage
The second case involves a hybrid storage system with both lithium battery and flywheel subsystems. The available site is 66.7 m × 43.6 m, and a road of width 5 m crosses the site vertically at a distance of 35.2 m from the left boundary. The system consists of five battery storage groups, each with one battery PCS cabinet and one energy storage battery cabinet, and two flywheel groups, each with one flywheel PCS cabinet and four flywheel cabinets (a one-to-four configuration). The dimensions and quantities are shown in the table below.
| Facility Type | Quantity | Dimensions (mm × mm) |
|---|---|---|
| Large EHV cabinet | 1 | 13400 × 3500 |
| Small EHV cabinet | 1 | 7000 × 3500 |
| LV cabinet | 1 | 12192 × 3000 |
| Station transformer cabinet | 1 | 5500 × 2800 |
| Battery PCS cabinet | 5 | 9125 × 2438 |
| Energy storage battery cabinet | 5 | 12192 × 2438 |
| Flywheel PCS cabinet | 2 | 16000 × 3800 |
| Flywheel cabinet | 8 | 5000 × 5000 |
The total number of facilities is 24. The initial solve time limit is 3 minutes. The initial weights are \(\alpha_0 = 0.7\), \(\beta_0 = 0.2\), \(\gamma_0 = 0.1\), and the final weights are \(\alpha_{\text{fin}} = 0.4\), \(\beta_{\text{fin}} = 0.4\), \(\gamma_{\text{fin}} = 0.2\). The initial population size \(M_0 = 24\), and \(M_1 = 25\).
In the initial population, the flywheel groups are already kept relatively close due to the safety and maintenance constraints. However, the lithium battery area is not yet well organized. After fixing one facility and re-solving, the layout improves considerably. One interesting phenomenon occurs when the algorithm fixes a flywheel-related facility: the objective function converges slowly, and the process appears to enter a local optimum. Visual inspection of the intermediate solution reveals that the left side of the site is poorly utilized, with unnecessary gaps between battery cabinets. The algorithm detects the lack of improvement (the relative decrease in the objective falls below 5% for two consecutive iterations) and triggers the unlocking mechanism. One of the fixed flywheel PCS cabinets is freed, and the optimization resumes. This allows the algorithm to escape from the local optimum and eventually find a better layout.
The final solution places the flywheel groups in the right-hand section of the site, well separated from the battery storage area. The battery cabinets and their corresponding PCS cabinets are aligned in neat rows on the left side of the road. The station transformer and LV cabinets are located near the top-left corner, close to the external grid connection point. This layout is both functional and aesthetically pleasing.
To demonstrate the numerical performance, I list the objective function values at key stages for both cases in the following table.
| Stage | Case 1 (17 facilities) | Case 2 (24 facilities) |
|---|---|---|
| Best initial objective | 1.000 (normalized) | 1.000 |
| Best objective after 2 fixed facilities | 0.938 | 0.915 |
| Final objective | 0.861 | 0.824 |
| Total computation time (min) | 12 | 35 |
These results demonstrate that the iterative locking strategy can effectively reduce the problem complexity and improve the solution quality over time. The method is particularly useful for hybrid systems where the presence of flywheels introduces strong non-linear grouping preferences.
5. Conclusions and Future Work
In this paper, I have presented a comprehensive layout design method for hybrid energy storage systems in thermal power plants. The core contribution is the integration of a mixed-integer linear programming model with a metaheuristic-driven iterative reduction strategy. The model incorporates practical engineering constraints such as safety clearances, obstacle avoidance, and non-overlap requirements, and optimizes a multi-objective function that balances cable cost, operational convenience, and aesthetics. The dynamic weighting mechanism allows the optimizer to evolve its preferences during the search, closely mimicking human design behavior.
I have validated the method on two real-world cases: a pure lithium battery system and a combined battery-flywheel system. In both cases, the algorithm produced high-quality layouts in reasonable computation times. In particular, the unlocking mechanism proved effective in escaping local optima that can arise when flywheel groups are over-constrained.
There are several directions for future research. First, current models assume that all facilities are axis-aligned rectangles. Real prefabricated cabinets may have protrusions or irregular shapes that require more detailed geometric modeling. Second, the site boundary is assumed to be rectangular, but actual power plant sites often have irregular boundaries or multiple disconnected buildable zones. Extending the model to handle arbitrary polygons would broaden its applicability. Third, I have not considered the joint optimization of internal road layouts and facility positions. In many retrofit projects, the positions and widths of access roads are not fixed and can be optimized simultaneously to reduce space waste. Fourth, new types of storage technologies, such as molten salt thermal storage, offer different layout requirements due to their large tanks and piping systems. Integrating these into the same optimization framework is a promising research direction.
Finally, although energy storage battery and flywheel systems have been the focus of this study, the proposed method is general enough to be adapted to other industrial facility layout problems with similar characteristics. The combination of exact solvers and metaheuristic strategies provides a practical trade-off between solution quality and computational effort, which is essential for real-world engineering design.
In summary, the rapid growth of hybrid energy storage applications demands efficient and systematic layout design tools. The method presented here advances the state of the art by providing a rigorous yet practical optimization approach. I believe that with further extensions and refinements, this framework can become a standard tool for the layout planning of energy storage systems in thermal power plants and other industrial settings.