Designing diversified renewable energy systems to balance multisector performance

Integrated river basin and power system simulation

The multisector simulation model integrates the independent river basin and the power system simulators. The system integration is implemented using the Python Network Simulation (Pynsim) library³³, which coordinates model inputs and outputs to form a single simulation at model run-time representing feedback across the models (see Supplementary Fig. 2). The integrated simulation considers spatially explicit sectoral infrastructure and connectivity within and between the models.

The models run sequentially with feedback across the models’ interconnections. In this study, hydropower connector nodes use unidirectional feedback; that is, the river basin model decides the hydropower releases and passes the information to the power system. The river basin model runs its first time step (a week) and generates the weekly average hydropower generation, which is transferred to the power system as a maximum generation capacity constraint for that week. The power system model runs for the same week at an hourly time step, constrained by the information provided by the river basin model. The river basin and power system models repeat this process, time step by time step until the completion of the simulation. The integrated model runs over a 10-year time horizon, from 2030 to 2040; the system performance metrics are calculated once a simulation is completed.

Electricity demand projections, generating resources, operating and capital costs, and hourly profiles of intermittent renewable resources were obtained from the Integrated Power System Master Plan for Ghana³⁷. Hourly load profiles and transmission data were provided by the Ghana Grid Company, which operates the national grid. Long-term projections for annual peak load are available in the Ghana Power System Master Plan³⁷. Those projections estimate a twofold increase in the peak load by 2030 compared with 2018. We scaled the hourly load profile of 2018 using the 2030 to 2040 peak projections to consider the projected increase in electricity demand in the country. Capital costs include engineering, procurement, construction, start-up costs and owner’s cost (land, cooling infrastructure, administrative and associated buildings, site works, project management and licenses)³⁷. The operating cost of intermittent renewable technologies is low enough, compared with the costs of hydropower, bioenergy and thermal plants, to ensure that intermittent renewable technologies’ economic dispatch follows the hourly generation profiles³⁷. We modelled PV with storage technology using an hourly PV generation profile, similarly to the way in which it was modelled in the Integrated Power System Master Plan for Ghana³⁷. The solar-with-storage profile takes out 30% of the PV generation profile during the daytime and discharges it during peak periods, following ref. ³⁷.

River basin model

The river basin model uses the open-source Python Water Resources (Pywr) simulation library³⁰. Pywr solves a linear program at every simulation time step deciding the optimal water allocation from different nodes in the system (for example, hydropower reservoir releases) by minimizing allocation penalties subject to operating rules. The model solves a mass balance equation (Eq. (1)) at each node in the network representing incremental catchment inflows and water demands at ecosystem service delivery and infrastructure locations:

where S_t,n is the volume of water stored in the reservoirs at node n, in time step t, and \(r_t,n^i\) is the water allocation for the water uses (i) in the system, public water supply (pws), hydropower (hp), and irrigation schemes (is). r_t,n is the sum of water releases for water uses (that is, public water supply, irrigation and hydropower), and \(\varphi _n\left( \cdot \right)\) are the reservoir operating rules, which constrain water allocation decisions. Irrigation demand is defined by the planted area of each crop (ct) that comprises an irrigation scheme. sp_t,n denotes spill flows from reservoirs; q_t,n are inflows to nodes, and \(e_t,n\left( \cdot \right)\) represents evaporation, which depends on water level h_t,n in reservoir. C^R is the network connectivity matrix \(\left[ {{\mathrmC}_\mathrmj,\mathrmk^{\mathrmR} = 1\left( – 1 \right)\mathrmwhen\,\mathrmthe\,\mathrmnode\,{\mathrmj}\,\mathrmreceives\,\mathrmwater\,\mathrmfrom\left( {\mathrmto} \right){\mathrmnode}\,{\mathrmk}} \right]\). For releases to irrigation schemes, the network connectivity matrix tracks flows that return to the network as a fraction of the releases. The model includes existing infrastructure in Ghana and Burkina Faso, including the Pwalugu multi-purpose dam, which is under construction. More details of the Volta River basin model can be found in ref. ³¹, a previous publication on the model.

Reservoir operating rules

We used Gaussian radial basis functions (RBFs) to represent reservoir operating rules. RBFs have shown good performance representing rules for diverse problems, including reservoir storage and time into release decisions^52,53,54,55. The Gaussian RBF is defined by Eq. (4):

where m = 2 is the number of input variable x (time and reservoir volume); l is the number of RBFs (l = 4); w_i is the weight of the ith RBF (φ_i); and c_j,i and b_j,i are the m-dimensional centres and radius vectors of the ith RBF, respectively. The centres and radius take values in \(c_j,\mathrmi \in \left[ – 1,1 \right]b_{j,\mathrmi} \in \left[ 0,1 \right]w_{j,\mathrmi} \in \left[ 0,1 \right]\mathop \sum\nolimits_{\mathrmi = 1}^\mathrmn {w_{{{\mathrmi}}}} = 1\). The parameter vector θ is defined as \(\mathbf\theta = \left[ {c_{j,{{{\mathrmi}}}},b_{j,{{{\mathrmi}}}},{{\mathrmw}}_{{{\mathrmi}}}} \right]\). In Eq. (4), the time and reservoir volume are mapped to decide a target reservoir release at each time of the simulation period.

Power system model of Ghana

The power system model simulates each time step (that is, hour) using a direct current optimal power flow linear program formulation (Eqs. 5, 6 and 7), described in ref. ³². The simulation minimizes power system costs as denoted by Eq. (5). Equation (6) represents the equality constraints (that is, power balance at each node), while Eq. (7) represents the inequality constraints (that is, power generation and line flow limits):

where u is the vector of control variables that includes the control active power output of a generation unit and load curtailment. x is the vector of state variables, including the voltage angle at each bus, and y is the vector of parameters such as connectivity, reactance and generator limits. OC_n is the operating cost per generator, P_t,n is the power output per generator in each time step of the simulation model, LC_t,n is the load curtailment, and PE is a load curtailment penalty. We simulate network connectivity and impedances, power generation technologies, locations and demand profiles.

Integrated river basin and power system design process

The multisector simulation model is connected to an artificial intelligence-based multi-objective evolutionary algorithm (MOEA) to perform a multi-objective trade-off analysis. This identifies the performance trade-offs of the most efficient (Pareto optimal) portfolios of synergistic WEFE system interventions without needing to pre-specify preferences or weights for the different objectives. This supports unbiased a posteriori decision-making^56,57,58; that is, where stakeholders can assess how much they value each dimension of performance by seeing the implied sacrifice to other dimensions. MOEAs are an established iterative population-based meta-heuristic search method that identifies a multi-dimensional non-dominated (‘best achievable’) set of objective solutions, using processes that mimic the natural evolutionary process to explore the search space and find the best performing combinations of options^56,57,59,60. Results assist policymakers and stakeholders in designing WEFE nexus resource systems by revealing to them the synergies and trade-offs of the most efficient bundles of interventions.

Performance metrics for the River basin model

Performance metrics used to quantify water use benefits include irrigation yields and revenues from irrigation schemes Eq. (11), flood recession agriculture benefits Eq. (14), and hydrological alteration produced by hydropeaking Eq. (16) (Richards–Baker flashiness index^14,41).

Basin irrigation yields are estimated using the Food and Agriculture Organization (FAO) Crop Water Requirements method⁶¹ for the following crops: sugar cane, maize, rice, beans, tomatoes and fresh vegetables.

where CWR_t,n is the crop water requirement per node (n) (irrigation scheme). \(Kc_t,(ct \in n)\), \(ETo_t,(ct \in n)\), and R_t,n are crop factors, reference crop evapotranspiration (in mm per day), and effective rainfall (in mm per day) obtained from ref. ⁶². \(A_(ct \in n)\) is the area (in ha) of each crop type. IWR_t,n is the irrigation water requirement per irrigation scheme, and α_ct and β_ct are irrigation and conveyance efficiencies (assumed to be 0.8 and 0.7, respectively, for surface irrigation). CR_t,n is the water supply curtailment ratio, y_n is annual crop yield (in tonnes per ha) per irrigation scheme, r_t,n is the crop water allocated by the river basin model, sy the number of simulated years, and f^Y is total irrigation crop yield (in tonnes per year). We used international crop prices to estimate the agricultural sector revenues from FAO.

Flood recession agriculture (FRA) depends on the floodplain’s seasonal flooding during the peak rainy season in northern Ghana (July to September). The magnitude of the annual peak determines the total area sown each year⁶³. Low flood peaks result in no overflowing of the riverbanks preventing flood recession activities. Once the flooding threshold is breached, the flooded area increases with the flood peak. Extreme floods negatively affect flood recession activities by removing fertile topsoil. The area suitable for flood recession agriculture reduces to zero for extreme flows (95% exceedance probability³¹):

where \(q_n^{{{{\mathrmFRA}}}}\) is the mean flow in August or September during the simulation horizon; q_t,n is the mean flow in August and September; \(A_n^f( \cdot )\) is flooded area (in ha); f_FRA is a suitability factor⁶³; C_y is crop yield (in tonnes per ha) assuming a typical flood recession agriculture crop mix of maize, beans, Bambara beans, soya, millet and groundnuts⁶⁴; Y_n is total FRA yield (in tonnes per year); β_FRA is average regional market price of crops at US$1,222 per tonne (ref. ⁶⁵); and f^FRA is the financial benefit (in US$) of flood recession agriculture activity.

Although variations in flow patterns produced by flood peaks and precipitation patterns are part of the natural flow regimen in streams, flow rates observed as a result of hydropeaking can show multiple peaks per day and intensities that exceed those of the strongest natural floods negatively impacting aquatic ecosystems⁶⁶. Sub-daily hydrological alteration is quantified using the Richards–Baker flashiness index⁴³. This index accounts for the sequence, magnitude and number of peaking events in a day of a hydropower plant¹⁴. The index used in this study does not account for seasonal changes induced by re-operating baseload hydropower plants. Natural sub-daily flows are characterized by a steady flow regime, with infrequent short-term fluctuations where native flora and fauna are adapted to various features of this natural flow regime; human alteration of flow regimens often impairs these biological communities^43,44,45. Thus, a high Richards–Baker (RB) flashiness index value implies a flashy stream (less natural flow) and a less desirable regime, whereas a low index value characterizes a stable stream^14,15,43,67. More details on the impacts of altering the flow river regime can be found in a review of refs. ^68,69:

Similarly to ref. ¹⁴, we calculate a daily Richards–Baker index aggregating hourly data, which is calculated as the sum of the difference between turbined flows qt_t of consecutive hours t and t + 1, normalized by the total turbined flow over time horizon Td = 24h. Consequently, if the simulation time horizon is 1 year at an hourly time step, a time series of 365 values of the Richards–Baker index is created. The Richards–Baker index \(\left( f_n^RB \right)\) is calculated for each hydropower plant (n).

Performance metrics for the power system model

The performance metrics used to quantify power system benefits and costs include system load curtailment (Eq. (17)), CO₂ emission (Eq. (18)), system capital costs (Eq. (19)) and system operating costs (Eq. (20)).

The system load curtailment (LC_t,n) is calculated by the power system simulation model at each time step when the balance at each bus (n) is performed. The balance at each bus in the system is modelled as a function of demand, generation, load curtailment and flows across the transmission lines. At the end of each simulation, the system load curtailment is calculated based on Eq. (17):

where sy is the number of simulation years and f^lc is the average system load curtailment.

To calculate the CO₂ emissions, we multiply the generation (P_t,n) from the power system simulator in each time step (t) and generator plant by a CO₂ emission factor⁷⁰ per generator technology (\(ft_n^\mathrmCO_2\)):

where f^OPEX is the average CO₂ emissions produced by the power system.

The system capital costs were calculated by multiplying the technology capital cost CC_n by the new infrastructure capacity (NI_n), which is selected in the multi-objective optimization process:

where f^CAPEX is the system capital expenditure.

To calculate the system operating costs, we multiply the operating cost per generator (CC_n) by the power output (P_t,n) per generation technology (n) in each time step (t):

where f^OPEX is the system operating expenditure.

Integrated WEFE resource system design problem

The integrated multi-objective optimization design solves the objective function presented in Eq. (21). The design formulation’s objectives include minimizing the system load curtailment (f^lc), the CO₂ emissions from generation \(\left( {f^{{\mathrmCO}_2}} \right)\), the power system capital costs (f^CAPEX), the system operating costs (f^OPEX), and the hydrological alteration downstream of the Akosombo, Bui and Pwalugu reservoirs \(\left( {f_n^{{\mathrmRB}}} \right)\). Also, the design problem maximizes the agricultural yields (f^Y) and the flow recession economic activities (f^FRA).

We use the Borg multi-objective evolutionary algorithm^71,72 to solve the multi-objective optimization design (Eq. 21). Borg handles complex non-linear and non-concave problems when searching for non-dominated solutions^72,73. The optimization process for each of ten random seeds follows two steps summarized in Supplementary Fig. 1: first, initialization of the Borg multi-objective evolutionary algorithm using a set of decision variables for the integrated simulation model (in our analysis, power system infrastructure capacity and reservoir operating rule parameters), and second, running the integrated WEFE simulation over the 10-year time horizon evaluating performance metrics and sending them back to the search algorithm. The optimization algorithm then selects a new set of decision variables for the next iteration. The first and second steps are repeated for a set number of evaluations of the objective function vector (Eq. (21)), in our case 700,000 iterations.

Three intervention strategies are defined to counter the variability of intermittent renewables from hourly to seasonal timescales. The intervention strategies are defined around the decision variables (y, θ_n) of the objective problem presented in Eq. (21), where y is a vector that combinates the expansion of different power system infrastructure—intermittent renewables (solar and wind), solar with storage, bioenergy and transmission lines—and θ_n is the vector of parameters of the reservoir operating rules presented in Eq. (4), which determines the hydropower plants’ re-operation. The different intervention strategies are shown in the following section.

Intervention strategy one

The decision variables in intervention scenario one are the vector of infrastructure expansion (y)—including solar, solar with storage and wind generators—and the vector of operating rules parameters (θ) for Akosombo, Bui and Kpong reservoirs. This intervention strategy aims to evaluate the impacts of the hydropower plants’ re-operation and their contribution to the integration of high levels of intermittent renewables. In this strategy, hydropower and thermal generation plants provide the power system flexibility necessary to integrate intermittent renewables. However, existing thermal and hydropower generation is constrained by the existing capacity of the transmission network of the power system.

Intervention strategy two

The decision variables in intervention strategy two are the vector of infrastructure expansion (y)—including solar, solar with storage and wind generators and transmission lines—and the vector of operating rules parameters (θ) for Akosombo, Bui and Kpong reservoirs. In this scenario, the transmission line capacity in the power system is a decision variable in the optimization problem. Here, the re-operation of hydropower plants and existing thermal generation also provide flexibility to the power system. However, expanding the transmission lines will allow the system to reallocate and distribute the renewable (intermittent or not) resources in the system to displace thermal generation and reduce CO₂ emissions.

Intervention strategy three

Finally, decision variables in intervention strategy three are the vector of infrastructure expansion (y)—including solar, solar with storage, wind and bioenergy generators and transmission lines—and the vector of operating rules parameters (θ) for Akosombo, Bui and Kpong reservoirs. In this strategy scenario, a new technology that provides system flexibility is included. This scenario constitutes a fully diversified power system infrastructure portfolio scenario of renewable (intermittent or not) resources advocated to reduce system CO₂ emissions, meet the increasing electricity demand, and reduce intersectoral conflicts in WEFE resource systems. Bioenergy (biogas and biomass) is considered in the design process because it is Ghana’s main renewable, dispatchable and spatially distributed technology. Just from crop residues, bioenergy potential has been estimated at around 75 TJ³⁷. Bioenergy in Ghana is available from residues from the various stages of agricultural and forestry activities, mainly from crop harvesting, wood logging and residues from municipal wastes and other commercial and domestic activities³⁷.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.