Vensim DSS version 6.2 was used to develop the model. WAPP member country level data elicited from WAPP and ECOWAS Regional Electricity Regulatory Authority (ERERA) serves as the set of basic data used to develop and run the main model ( Figure 4). Other data elicited from various journal articles and internet sources (Central Banks of ECOWAS Member State Countries; Bureau of Statistics; Electricity Regulatory Bodies) include population and its average growth rate, GDP, per capita income, average per capita electricity demand, electricity generated, average electricity tariff, generation technology type, amongst others. The generated SD model examines the (nonlinear) relationship regarding generation adequacy and GHG emission reduction in the WAPP. It evaluated the strain of providing adequate supply capacity as against emission reduction from the generation technologies in the West Africa electricity system. The complexities in the West African electricity system were arranged in the model to establish the basic interconnecting structure for the system analysis; this is to achieve global expectations of emission reduction and economic growth.

SD Model for planning in the WAPP system is shown in Figure 4. The model development was guided with CLD and SFD as explained in earlier sections depicted in Figure 2 and Figure 3. Its structure was developed with the boundary set around electricity supply, generation and marketing, population and the GDP. This was achieved through WAPP electricity system operations review. The model focuses largely on interconnections in the WAPP power system regarding its operations and GHG emission. The power system examined emission from the basis of generation and average emission factor as well as based on generation technology types.

The first assumption to developing the model is that the different regulatory authorities in the WAPP system are responsible for reviewing proposals submitted for building of new power plants. Second assumption in order to ease the model development is that these authorities all have uniform modus operandi. The first step is that applications to construct new power plants by would-be investors accumulate to regulatory authorities for approval or rejection. The time needed to process proposals depends on both capacity of examining multiple projects and project complexities, such as proposed technologies (e.g. nuclear, hydro, CCGT) and the specific siting of the new power station. This process could take some time depending on the technology type being processed. The normal assumption is that when the permits are granted, would-be investor will construct the power plants due to inadequacy in the system currently. In order to achieve balancing feedback, time delay is assumed to be reduced to provide a higher stability margin to the system. Nevertheless, when new efficient plants in pipeline are finished and start to generate, prices may not be depressed for older plants as they are under long term contract and will not likely exit business. The effect of this is increase in the rate of aging in the available stocks, which has positive effect on the reserve margin. However, the growth of electricity demand is expected to impact on reserve margin negatively, causing a new wave of constructions due to both accumulated permits and a stream of new proposals. For accumulated permits, starts are immediate; stream of new proposals would have to face delay in the time needed to obtain permits. This implies that though decision of investing in new plants may be simultaneous, it will however have a different time-phase for the market place.

The stock-and-flow structure must be further expanded in parallel stock chains in order to consider the different characteristics of the several available technologies. Since the stocks represent different stages of the power plant operations such as the installed capacity, the capacity under construction, etc., this have to be disaggregated to account for different lifetimes, construction lead-times, permitting delays, etc. In addition to this disaggregation, for the same generating technology, installed capacity has to be distinguished by age to keep track of thermal efficiencies, and therefore, the spread in marginal cost of production.

With the foregoing, the first step to developing the SD model is to assemble and analyze an array of data pertaining to the electric power sector in the WAPP (see 23). This step helped to understand the interconnections in the system that affects its performance. From these interconnections, is developed the causal-loop diagram ( Figure 5). This simplifies the development of stock and flow diagram that make up the model. With the stock and flow diagram, the set of equations driven the model to run were derived.

Models developed in Vensim are capable of using time frame of seconds to many years, depending on the kind of system being evaluated in the model. The time frame used for developing this model to evaluate the long-term performance of the WAPP system is 50 years, 2015 to 2064. This can be changed within the model setting. Evaluating the long-term performance of WAPP system requires developing a model that takes the dynamics of the structure and behaviour of the system into consideration. Having realized this need from the onset, SD technique was chosen using Vensim 6.2 software platform, which is one of the recognized software platforms with capability for developing such model ( http://www.vensim.com/sdmail/sdsoft.html; Wikipedia website). To develop this model, the main ideas made use of Ford study ^{25, 26} as well that in Oyebisi and Momodu ²³ . The model assumes that the WAPP will act as one market, where price of electricity would be driven be driven by demand and supply, that is, levelised energy cost as well as future retail tariff. Demand of electricity is based on WAPP forecasting data.

Figure 4 shows the causal loop diagram showing the interconnections in the Nigerian electricity system ²⁴ . This was adopted for the WAPP system. Following from knowing this structure and behaviour characteristics, the first step to developing the model was to make use of historical data available for performance of the system. These include its installed capacity (taking different technology in the generation park into consideration), availability factor, capacity factor, peak load, energy generated, transmission capacity, losses (transmission, distribution, non-technical and non-billed energy sent out), and energy sold. This formed the baseline information data to develop the model. Other parameters that were developed for the baseline include gross domestic product and population of the country. From the baseline information other variables which contribute to the structure and behaviour of the system were added. These include capacity addition, future capacity needed, and regulated tariff. Having developed the model based on the baseline information, other parameters needed were then calculated. This ensures both validation and robustness of the model to explain the behaviour of the WAPP system.

There are quite a number of variables for estimating future population depending on the finer details needed. However, the most striking variables are those of fertility and mortality rates ²⁷ . In this study, a simple approach of birth and death was used to develop a future population trend for Nigeria. Future birth per year of the existing population is a factor driven by birth rate, while death is regulated by average life expectancy. Mathematically, this is represented in the model as:

P o p u l a t i o n = ∫ t = 1 t = 36 ( b i r t h − d e a t h )

where

b i r t h t + 1 = b i r t h r a t e t + 1 × P o p u l a t i o n t , and

d e a t h = a v e r a g e   l i f e e x p e c t a n c y t   + 1   × P o p u l a t i o n

The dynamics of the model is then described by a set of non-linear differential equations that account for existing system feedbacks, delays, stock-and-flow structures and nonlinearities. What makes the model to stand out is that its various sectors and spheres are connected together to as a complex link of feedback loops. This allows the electric system to be analyzed and weighted as a driving or limiting factor for LCD agenda in any country.

A major principle in the developed SD model is the leverage points. “ Leverage points are places within a complex system (a corporation, an economy, a living body, a city, an ecosystem) where a small shift in one thing can produce big changes in everything” (see Donella Meadows Project page on leverage points). For SD model, the leverage points are points of importance in a system that modelers not only believe in but would be glad to know where they exist and how to locate them.

The “state of the system” — electricity, a nonmaterial commodity - in whatever standing stock is of importance. The stock is increased by inflow - electricity generation, investment and financial flow; while the outflow decreases it - transmission, distribution, losses and thefts. So, the bedrock of this system consists of physical stocks and flows, obeying the laws of conservation and accumulation. WAPP power system has inadequacy; simply interpreted to mean inflow rate is lower than the outflow rate. In other words, the non-storable commodity is always in shortfall.

Systems respond at a slower rate to desired growth rate as is typical for flows to accumulate. Electricity system in the WAPP exhibits the same characteristics; it will take time to correct the anomalies, being sluggish in responding to desired changes. This sluggishness is referred to as delay in the system. To achieve a quick turnaround in the system, it is critical to identify the 'leverage points' along the line of the operations of the WAPP electricity system. This takes into consideration the superimposed LCD strategy in the model as corrective measures to achieve change in the system.

At least two negative feedback loops, or correcting loops exist in a system ^{13– 15, 28} ; the first is what controls the inflow, and the second, controls the outflow. Either or both can be used to bring the system to a desired level. Usually, the goal and the feedback connections are not visible in the system except when viewed from long-term perspective to figure out what are the leverage points in it. In this study a new paradigm - LCD – was superimposed into the planning of an already complex WAPP system. This is with the desire for a future responsive plan amenable for delivering globally cost competitive electricity with reduced emission.

There are three interconnected sectors in the model. The sectors are electricity (split into capacity addition (MW) and power demand (GWh)), demography (principally the population) (persons), economy as depicted by the gross domestic product (GDP) (Billion US$), make up the three modules in the model. There are two sub-modules in the model as offshoot from the power demand segment under the electricity module. These are: emission from electricity consumption (tCO ₂) and electricity marketing (US$). Analysis of results from the model was limited to only the electricity module as data needed from other two modules narrowed the integrity of their results.

Each of the modules has at least one Level variable with integral equation. Most level variable equations in Vensim ^® software take the form of:

Level Variable (Name) = ∫ ( Inflow ( t) – Outflow ( t), initial _ value ( 0)

Level variables represent stocks in system dynamic models ^{14, 15} . This means that all the Level variables in the model, namely, Population, GDP, Capacity under Construction, and Grid Generation Capacity are stock operating the Principle of Accumulation ³ , and take on the form of Equation (1) to run in the model. Now, the critical aspect of Level variable is that it allows for the introduction of the concept of delay, a dynamic function, into the system being modeled. Being stocks, these variables have four important characteristics of having memory, changing the time shape of flows, decouple flows and create delays. The concept of delay is expatiated upon elsewhere ²² . One of the principal equations is that of Grid Generation Capacity as represented thus:

What is placed in the [X] shows the subscripts to the equation. This allows one variable and equation to represent a number of different distinct concepts.

The grid segment has capacity under construction to reflect how capacity is increased over the years. The grid capacity segment also has scrapping, which is driven principally by capacity life time (Years). The critical aspect of the capacity under construction is the assessment of initiating capacity, which in turn is driven by target capacity (MW) and time to adjust (Years). The target capacity is driven by per capita power generation in the system. The per capita power generation (kWh/Person) in the system is assumed to be driven principally by population (this is derived from the demography segment of the model). (In a fully liberalized market, this is expected to be determined by investor behavior - e.g. see 22).

It is important to state that the modules in the model are subscripted. Subscript in the modules allowed a variable (e.g. grid capacity, birth rate, GDP, etc.) to represent more than just a data for the variable. In this model, the subscript dealt with WAPP member country level information as well as aggregation of generation technology types in the WAPP.

Parameters within the model forms the basis for developing the scenarios for analysis. For the description in this chapter, two scenarios on the WAPP electricity system, Base Case and LCD Options, are examined. The Base Case scenario represents continuing a "business-as-usual" approach that draws on technologies in the electricity system as they currently are. No consideration is given for efficiency and how these technologies fare in terms of contribution to global warming through emission of GHG into the atmosphere. In the LCD Options, higher efficiency technologies emitting low carbon are drawn upon to replace generation technologies with high emitting factors. The LCD Option is examined based on changes in two parameters, namely, capacity and emission factors, against two different values of per capita electricity generation levels respectively. Other parameters are kept constant as in Base Case Scenario. To improve on the WAPP system, the LCD Option 1 was assumed to have emission factor improved by 10%, meaning EF is reduced by a factor of 0.1 from that of the Base Scenario, for each of the plants, while for LCD Option 2, it is reduced by a factor of 0.3.

The model is made up of seven subscripted ⁴ parameters, with the Base Case values listed in Table 1 being country level data and Table 2 being aggregated technology type in the WAPP. The high leverage points for policy intervention were identified from Table 1 and Table 2. High leverage points are places within a complex system (a corporation, an economy, a living body, a city, an ecosystem) where a small shift in one thing can produce big changes in everything else ²⁹ . Further testing - sensitivity analysis - could be conducted on the model. The high leverage points are parameters in the model as constants to conduct the sensitivity analysis. Sensitivity testing is the process of changing assumptions about the value of constants in the model and examining the resulting output (see 2010 System Dynamics conference site).

Multivariate sensitivity simulation (MVSS) or Monte Carlo simulation is a natural choice where multiple parameters are identified in the model as high leverage points. Four high leverage points identified in the West African electricity system are capacity factor (CF), emission factor (EF) (country average and technology type), time to adjust capacity and expectation formation. In running of the model, two parameters stood out on their effect on generation capacity addition and GDP.

More description of the parameter “time to adjust capacity” can be found in Momodu ² .

To achieve development, energy consumption would need to be increased. This means expansion of grid capacity in generation, transmission and distribution. So, at first glance as shown in Table 2, what is gleaned from the SDM is that development policies will be running counter to reducing GHG emission. Thus, to counter such direction it becomes necessary to apply a strategy that procures low carbon. This strategy will handle tension between achieving development and reducing GHG emissions from infrastructural provision. LCDS then becomes a means to achieve balancing of factors for policies that affect development and those that meant for climate change control. LCDS is counterintuitive, because it recognizes the existence of negative feedback loops. This is demonstrated in the result shown in Table 2. The Base Scenario guided how mitigation targets were set.

To examine low hanging options available for achieving LCDS in the WAPP electricity system, the two other alternatives were run for the LCD Option, namely, LCD Option 1 and 2 respectively. The first alternative considered increased efficiency in the generation capacity by a factor of 50%, through improved average capacity factor across the countries.

The second alternative, considered reduced emission through reducing average emission factor across WAPP member by 30%. This is in addition to the strategy adopted in LCD option 1. In the first alternative, the system gained increased energy generation, though with corresponding increase in emission as shown in Table 3. Still on Table 3, for LCD Option 2, when the average emission released from these plants were improved upon through across board 30% reduction in the emission factors, a reduced emission was achieved compared to merely improving the capacity factor. The energy generated in both alternatives, however, were similar. These two low-hanging alternatives analyzed were first identified as high leverage points from conducting the base run simulation.

The strategic intervention examined is for improved capacity and emission factors respectively. All other identified parameters are kept at their Base run values. For the electricity sector, this intervention is seen as low hanging option to address the trade-offs between economic development and emission reduction as options for targeting low carbon economy in West Africa. The possible barriers to achieving this intervention include but not limited to the following: (1)

not being ready to promote the technical knowhow needed to achieve desired improvement in the capacity and emission factor levels amongst the existing power generation technologies across the nations in WAPP;

To estimate the cost impact, only existing technologies were examined without taking into consideration environmental factor improvement such as carbon capture storage alongside the generation of new technology. Further, the estimate of cost impact was based on an across board average having combined the overnight cost ^{28, 29} for all existing generation technologies in West Africa, namely, oil, natural gas, coal and hydro.

The cost impact was calculated based on construction of new power plants. Factors determining new power plants cost are: environmental regulations, construction costs, financing costs and fuel expense. Other factors that drive power plants cost are government incentives, air emissions control on coal and natural gas.

Figure 6 is the mini model developed to assess the cost impact of these trade-offs. It was assumed that compounded annual initializing (growth) rate and compounded annual scraping rate in the system will be 6% and 1.5% respectively. Cost values were taken from 29, 30. Table 4 shows the cost impact for 2064. Total cumulative cost impact is approximately US$1.54 trillion from 2018 through to 2064. The cost impact was limited to capital, financing and fuel costs ^{27, 28} to estimate what is needed to achieve trade-offs in the WAPP system. This means that the total cost will be significantly higher than what is estimated here.

It is pertinent to point out that the cost estimates are based on OECD standard. The cost of this same technologies from other regions may be more competitive. Now, the existing mix of generation technologies in the WAPP system consists of oil-fired, natural gas, coal and hydro plants. The generators are not new and they have aged, and over the years, have been affected by changes in technology and economics. Indeed, most of the plants in the WAPP system have units that were built decades ago as base-load stations. Though still being operated as base-load ^{5, 31} (see Emission Factors site), they are best to be described as cycling or peaking plants. They have high fuel prices and poor efficiency, making them economically marginal. This implies that the regional organization will need to get the government of WAPP member nations involved to incentivize the strategic intervention process to for LCDS.

The government in this region must decide to deliberately influence the factors affecting cost of electricity to determine the kind of improvement that could be achieved in existing plants and/or power plants that would be built in the future. The first step would be to encourage the policy of energy efficiency through technological improvement with increased capacity factor and decreased energy intensity of economic activities that will also mean reduced emission factor. To encourage energy efficiency and decrease energy intensity of economic activities will both require increased spending on research and development on the part of government. This is currently non-existent in the West African region. The second strategy should be aimed at incentivizing construction of power plants to especially benefit base-load plants such as those that will encourage emission reduction, which are costly to build. The third approach which will be short term, say in a five-year period, that will allow low carbon fuels (principally, natural gas) cost to benefit intermediate load plants as a transition process; though inexpensive to build they have high variable cost due to fuel expense. This is to encourage a quick ramp up of generation capacity to increase economic dispatch in the grid system. These strategies should however be reviewed periodically in line with determination to meet Paris Agreement on NDC for these nations.